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Law

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For other uses, see Law (disambiguation) and Legal (disambiguation).
Lady Justice is the symbol of the judiciary.[1][2] Justice is depicted as a goddess equipped with three symbols of the rule of law: a sword symbolizing the court's coercive power; scales representing the weighing of competing claims; and a blindfold indicating impartiality.[3]

Law[4] is a system of rules, usually enforced through a set of institutions.[5] It shapes politics, economics and society in numerous ways and serves as a primary social mediator of relations between people. Contract law regulates everything from buying a bus ticket to trading on derivatives markets. Property law defines rights and obligations related to the transfer and title of personal (often referred to as chattel) and real property. Trust law applies to assets held for investment and financial security, while tort law allows claims for compensation if a person's rights or property are harmed. If the harm is criminalised in a statute, criminal law offers means by which the state can prosecute the perpetrator. Constitutional law provides a framework for the creation of law, the protection of human rights and the election of political representatives. Administrative law is used to review the decisions of government agencies, while international law governs affairs between sovereign nation states in activities ranging from trade to environmental regulation or military action. Writing in 350 BC, the Greek philosopher Aristotle declared, "The rule of law is better than the rule of any individual."[6]

Legal systems elaborate rights and responsibilities in a variety of ways. A general distinction can be made between civil law jurisdictions, which codify their laws, and common law systems, where judge made law is not consolidated. In some countries, religion still informs the law. Law provides a rich source of scholarly inquiry, into legal history, philosophy, economic analysis or sociology. Law also raises important and complex issues concerning equality, fairness and justice. "In its majestic equality", said the author Anatole France in 1894, "the law forbids rich and poor alike to sleep under bridges, beg in the streets and steal loaves of bread."[7] In a typical democracy, the central institutions for interpreting and creating law are the three main branches of government, namely an impartial judiciary, a democratic legislature, and an accountable executive. To implement and enforce the law and provide services to the public, a government's bureaucracy, the military and police are vital. While all these organs of the state are creatures created and bound by law, an independent legal profession and a vibrant civil society inform and support their progress.
Contents
[hide]

* 1 Legal subjects
o 1.1 International law
o 1.2 Constitutional and administrative law
o 1.3 Criminal law
o 1.4 Contract law
o 1.5 Tort law
o 1.6 Property law
o 1.7 Equity and trusts
o 1.8 Further disciplines
* 2 Legal systems
o 2.1 Civil law
o 2.2 Common law and equity
o 2.3 Religious law
* 3 Legal theory
o 3.1 History of law
o 3.2 Philosophy of law
o 3.3 Economic analysis of law
o 3.4 Sociology of law
* 4 Legal institutions
o 4.1 Judiciary
o 4.2 Legislature
o 4.3 Executive
o 4.4 Military and police
o 4.5 Bureaucracy
o 4.6 Legal profession
o 4.7 Civil society
* 5 See also
* 6 Notes
* 7 References
* 8 External links

[edit] Legal subjects

All legal systems deal with the same basic issues, but each country categorises and identifies its legal subjects in different ways. A common distinction is that between "public law" (a term related closely to the state, and including constitutional, administrative and criminal law), and "private law" (which covers contract, tort and property).[8] In civil law systems, contract and tort fall under a general law of obligations, while trusts law is dealt with under statutory regimes or international conventions. International, constitutional and administrative law, criminal law, contract, tort, property law and trusts are regarded as the "traditional core subjects",[9] although there are many further disciplines which may be of greater practical importance.
[edit] International law
Main articles: Public international law, Conflict of laws, and European Union law
Providing a constitution for public international law, the United Nations system was agreed during World War II

International law can refer to three things: public international law, private international law or conflict of laws and the law of supranational organisations.

* Public international law concerns relationships between sovereign nations. The sources for public international law development are custom, practice and treaties between sovereign nations, such as the Geneva Conventions. Public international law can be formed by international organisations, such as the United Nations (which was established after the failure of the League of Nations to prevent the Second World War),[10] the International Labour Organisation, the World Trade Organisation, or the International Monetary Fund. Public international law has a special status as law because there is no international police force, and courts (e.g. the International Court of Justice as the primary UN judicial organ) lack the capacity to penalise disobedience.[11] However, a few bodies, such as the WTO, have effective systems of binding arbitration and dispute resolution backed up by trade sanctions.[12]

* Conflict of laws (or "private international law" in civil law countries) concerns which jurisdiction a legal dispute between private parties should be heard in and which jurisdiction's law should be applied. Today, businesses are increasingly capable of shifting capital and labour supply chains across borders, as well as trading with overseas businesses, making the question of which country has jurisdiction even more pressing. Increasing numbers of businesses opt for commercial arbitration under the New York Convention 1958.[13]

* European Union law is the first and, so far, only example of a supranational legal framework. Given the trend of increasing global economic integration, many regional agreements—especially the Union of South American Nations—are on track to follow the same model. In the EU, sovereign nations have gathered their authority in a system of courts and political institutions. These institutions are allowed the ability to enforce legal norms both against or for member states and citizens in a manner which is not possible through public international law.[14] As the European Court of Justice said in the 1960s, European Union law constitutes "a new legal order of international law" for the mutual social and economic benefit of the member states.[15]

[edit] Constitutional and administrative law
Main articles: Constitutional law and Administrative law
The French Declaration of the Rights of Man and of the Citizen, whose principles still have constitutional value

Constitutional and administrative law govern the affairs of the state. Constitutional law concerns both the relationships between the executive, legislature and judiciary and the human rights or civil liberties of individuals against the state. Most jurisdictions, like the United States and France, have a single codified constitution, with a Bill of Rights. A few, like the United Kingdom, have no such document. A "constitution" is simply those laws which constitute the body politic, from statute, case law and convention. A case named Entick v Carrington[16] illustrates a constitutional principle deriving from the common law. Mr Entick's house was searched and ransacked by Sheriff Carrington. When Mr Entick complained in court, Sheriff Carrington argued that a warrant from a Government minister, the Earl of Halifax, was valid authority. However, there was no written statutory provision or court authority. The leading judge, Lord Camden, stated that,

The great end, for which men entered into society, was to secure their property. That right is preserved sacred and incommunicable in all instances, where it has not been taken away or abridged by some public law for the good of the whole ... If no excuse can be found or produced, the silence of the books is an authority against the defendant, and the plaintiff must have judgment.[17]

The fundamental constitutional principle, inspired by John Locke, holds that the individual can do anything but that which is forbidden by law, and the state may do nothing but that which is authorised by law.[18][19] Administrative law is the chief method for people to hold state bodies to account. People can apply for judicial review of actions or decisions by local councils, public services or government ministries, to ensure that they comply with the law. The first specialist administrative court was the Conseil d'État set up in 1799, as Napoleon assumed power in France.[20]
[edit] Criminal law
Main article: Criminal law

Criminal law, also known as penal law, pertains to crimes and punishment.[21] It thus regulates the definition of and penalties for offences found to have a sufficiently deleterious social impact but, in itself, makes no moral judgement on an offender nor imposes restrictions on society that physically prevents people from commiting a crime in the first place.[22] Investigating, apprehending, charging, and trying suspected offenders is regulated by the law of criminal procedure.[23] The paradigm case of a crime lies in the proof, beyond reasonable doubt, that a person is guilty of two things. First, the accused must commit an act which is deemed by society to be criminal, or actus reus (guilty act).[24] Second, the accused must have the requisite malicious intent to do a criminal act, or mens rea (guilty mind). However for so called "strict liability" crimes, an actus reus is enough.[25] Criminal systems of the civil law tradition distinguish between intention in the broad sense (dolus directus and dolus eventualis), and negligence. Negligence does not carry criminal responsibility unless a particular crime provides for its punishment.[26][27]
A depiction of a 1600s criminal trial, for witchcraft in Salem

Examples of crimes include murder, assault, fraud and theft. In exceptional circumstances defences can apply to specific acts, such as killing in self defence, or pleading insanity. Another example is in the 19th century English case of R v Dudley and Stephens, which tested a defence of "necessity". The Mignonette, sailing from Southampton to Sydney, sank. Three crew members and Richard Parker, a 17 year old cabin boy, were stranded on a raft. They were starving and the cabin boy was close to death. Driven to extreme hunger, the crew killed and ate the cabin boy. The crew survived and were rescued, but put on trial for murder. They argued it was necessary to kill the cabin boy to preserve their own lives. Lord Coleridge, expressing immense disapproval, ruled, "to preserve one's life is generally speaking a duty, but it may be the plainest and the highest duty to sacrifice it." The men were sentenced to hang, but public opinion was overwhelmingly supportive of the crew's right to preserve their own lives. In the end, the Crown commuted their sentences to six months in jail.[28]

Criminal law offences are viewed as offences against not just individual victims, but the community as well.[22] The state, usually with the help of police, takes the lead in prosecution, which is why in common law countries cases are cited as "The People v ..." or "R (for Rex or Regina) v ..." Also, lay juries are often used to determine the guilt of defendants on points of fact: juries cannot change legal rules. Some developed countries still condone capital punishment for criminal activity, but the normal punishment for a crime will be imprisonment, fines, state supervision (such as probation), or community service. Modern criminal law has been affected considerably by the social sciences, especially with respect to sentencing, legal research, legislation, and rehabilitation.[29] On the international field, 108 are members of the International Criminal Court, which was established to try people for crimes against humanity.[30]
[edit] Contract law
Main article: Contract
The famous Carbolic Smoke Ball advertisement to cure influenza was held to be a unilateral contract

Contract law concerns enforceable promises, and can be summed up in the Latin phrase pacta sunt servanda (agreements must be kept).[31] In common law jurisdictions, three key elements to the creation of a contract are necessary: offer and acceptance, consideration and the intention to create legal relations. In Carlill v Carbolic Smoke Ball Company a medical firm advertised that its new wonder drug, the smokeball, would cure people's flu, and if it did not, the buyers would get £100. Many people sued for their £100 when the drug did not work. Fearing bankruptcy, Carbolic argued the advert was not to be taken as a serious, legally binding offer. It was an invitation to treat, mere puff, a gimmick. But the court of appeal held that to a reasonable man Carbolic had made a serious offer. People had given good consideration for it by going to the "distinct inconvenience" of using a faulty product. "Read the advertisement how you will, and twist it about as you will", said Lord Justice Lindley, "here is a distinct promise expressed in language which is perfectly unmistakable".[32]

"Consideration" indicates the fact that all parties to a contract have exchanged something of value. Some common law systems, including Australia, are moving away from the idea of consideration as a requirement. The idea of estoppel or culpa in contrahendo, can be used to create obligations during pre-contractual negotiations.[33] In civil law jurisdictions, consideration is not required for a contract to be binding.[34] In France, an ordinary contract is said to form simply on the basis of a "meeting of the minds" or a "concurrence of wills". Germany has a special approach to contracts, which ties into property law. Their 'abstraction principle' (Abstraktionsprinzip) means that the personal obligation of contract forms separately from the title of property being conferred. When contracts are invalidated for some reason (e.g. a car buyer is so drunk that he lacks legal capacity to contract)[35] the contractual obligation to pay can be invalidated separately from the proprietary title of the car. Unjust enrichment law, rather than contract law, is then used to restore title to the rightful owner.[36]
[edit] Tort law
Main article: Tort
The "McLibel" two were involved in the longest running case in UK history for publishing a pamphlet criticising McDonald's restaurants.

Torts, sometimes called delicts, are civil wrongs. To have acted tortiously, one must have breached a duty to another person, or infringed some pre-existing legal right. A simple example might be accidentally hitting someone with a cricket ball.[37] Under the law of negligence, the most common form of tort, the injured party could potentially claim compensation for his injuries from the party responsible. The principles of negligence are illustrated by Donoghue v Stevenson.[38] A friend of Mrs Donoghue ordered an opaque bottle of ginger beer (intended for the consumption of Mrs Donoghue) in a café in Paisley. Having consumed half of it, Mrs Donoghue poured the remainder into a tumbler. The decomposing remains of a snail floated out. She claimed to have suffered from shock, fell ill with gastroenteritis and sued the manufacturer for carelessly allowing the drink to be contaminated. The House of Lords decided that the manufacturer was liable for Mrs Donoghue's illness. Lord Atkin took a distinctly moral approach, and said,

The liability for negligence ... is no doubt based upon a general public sentiment of moral wrongdoing for which the offender must pay ... The rule that you are to love your neighbour becomes in law, you must not injure your neighbour; and the lawyer's question, Who is my neighbour? receives a restricted reply. You must take reasonable care to avoid acts or omissions which you can reasonably foresee would be likely to injure your neighbour.[39]

This became the basis for the four principles of negligence; (1) Mr Stevenson owed Mrs Donoghue a duty of care to provide safe drinks (2) he breached his duty of care (3) the harm would not have occurred but for his breach and (4) his act was the proximate cause, or not too remote a consequence, of her harm.[38] Another example of tort might be a neighbour making excessively loud noises with machinery on his property.[40] Under a nuisance claim the noise could be stopped. Torts can also involve intentional acts, such as assault, battery or trespass. A better known tort is defamation, which occurs, for example, when a newspaper makes unsupportable allegations that damage a politician's reputation.[41] More infamous are economic torts, which form the basis of labour law in some countries by making trade unions liable for strikes,[42] when statute does not provide immunity.[43]
[edit] Property law
Main article: Property law
A painting of the South Sea Bubble, one of the world's first ever speculations and crashes, led to strict regulation on share trading.[44]

Property law governs valuable things that people call 'theirs'. Real property, sometimes called 'real estate' refers to ownership of land and things attached to it.[45] Personal property, refers to everything else; movable objects, such as computers, cars, jewelry, and sandwiches, or intangible rights, such as stocks and shares. A right in rem is a right to a specific piece of property, contrasting to a right in personam which allows compensation for a loss, but not a particular thing back. Land law forms the basis for most kinds of property law, and is the most complex. It concerns mortgages, rental agreements, licences, covenants, easements and the statutory systems for land registration. Regulations on the use of personal property fall under intellectual property, company law, trusts and commercial law. An example of a basic case of most property law is Armory v Delamirie.[46] A chimney sweep's boy found a jewel encrusted with precious stones. He took it to a goldsmith to have it valued. The goldsmith's apprentice looked at it, sneakily removed the stones, told the boy it was worth three halfpence and that he would buy it. The boy said he would prefer the jewel back, so the apprentice gave it to him, but without the stones. The boy sued the goldsmith for his apprentice's attempt to cheat him. Lord Chief Justice Pratt ruled that even though the boy could not be said to own the jewel, he should be considered the rightful keeper ("finders keeper") until the original owner is found. In fact the apprentice and the boy both had a right of possession in the jewel (a technical concept, meaning evidence that something could belong to someone), but the boy's possessory interest was considered better, because it could be shown to be first in time. Possession may be nine tenths of the law, but not all.

This case is used to support the view of property in common law jurisdictions, that the person who can show the best claim to a piece of property, against any contesting party, is the owner.[47] By contrast, the classic civil law approach to property, propounded by Friedrich Carl von Savigny, is that it is a right good against the world. Obligations, like contracts and torts are conceptualised as rights good between individuals.[48] The idea of property raises many further philosophical and political issues. Locke argued that our "lives, liberties and estates" are our property because we own our bodies and mix our labour with our surroundings.[49]
[edit] Equity and trusts
Main articles: Equity (law) and Trust law
The Court of Chancery, London, early 19th century

Equity is a body of rules that developed in England separately from the "common law". The common law was administered by judges. The Lord Chancellor on the other hand, as the King's keeper of conscience, could overrule the judge made law if he thought it equitable to do so.[50] This meant equity came to operate more through principles than rigid rules. For instance, whereas neither the common law nor civil law systems allow people to split the ownership from the control of one piece of property, equity allows this through an arrangement known as a 'trust'. 'Trustees' control property, whereas the 'beneficial' (or 'equitable') ownership of trust property is held by people known as 'beneficiaries'. Trustees owe duties to their beneficiaries to take good care of the entrusted property.[51] In the early case of Keech v Sandford[52] a child had inherited the lease on a market in Romford, London. Mr Sandford was entrusted to look after this property until the child matured. But before then, the lease expired. The landlord had (apparently) told Mr Sandford that he did not want the child to have the renewed lease. Yet the landlord was happy (apparently) to give Mr Sandford the opportunity of the lease instead. Mr Sandford took it. When the child (now Mr Keech) grew up, he sued Mr Sandford for the profit that he had been making by getting the market's lease. Mr Sandford was meant to be trusted, but he put himself in a position of conflict of interest. The Lord Chancellor, Lord King, agreed and ordered Mr Sandford should disgorge his profits. He wrote,

I very well see, if a trustee, on the refusal to renew, might have a lease to himself few trust-estates would be renewed ... This may seem very hard, that the trustee is the only person of all mankind who might not have the lease; but it is very proper that the rule should be strictly pursued and not at all relaxed.

Of course, Lord King LC was worried that trustees might exploit opportunities to use trust property for themselves instead of looking after it. Business speculators using trusts had just recently caused a stock market crash. Strict duties for trustees made their way into company law and were applied to directors and chief executive officers. Another example of a trustee's duty might be to invest property wisely or sell it.[53] This is especially the case for pension funds, the most important form of trust, where investors are trustees for people's savings until retirement. But trusts can also be set up for charitable purposes, famous examples being the British Museum or the Rockefeller Foundation.
[edit] Further disciplines

Law spreads far beyond the core subjects into virtually every area of life. Three categories are presented for convenience, though the subjects intertwine and overlap.

Law and society

A trade union protest by UNISON while on strike

* Labour law is the study of a tripartite industrial relationship between worker, employer and trade union. This involves collective bargaining regulation, and the right to strike. Individual employment law refers to workplace rights, such as job security,health and safety or a minimum wage.
* Human rights, civil rights and human rights law are important fields to guarantee everyone basic freedoms and entitlements. These are laid down in codes such as the Universal Declaration of Human Rights, the European Convention on Human Rights (which founded the European Court of Human Rights) and the U.S. Bill of Rights. The Treaty of Lisbon makes the Charter of Fundamental Rights of the European Union legally binding in all member states except Poland and the United Kingdom.[54]
* Civil procedure and criminal procedure concern the rules that courts must follow as a trial and appeals proceed. Both concern a citizen's right to a fair trial or hearing.
* Evidence law involves which materials are admissible in courts for a case to be built.
* Immigration law and nationality law concern the rights of foreigners to live and work in a nation-state that is not their own and to acquire or lose citizenship. Both also involve the right of asylum and the problem of stateless individuals.
* Social security law refers to the rights people have to social insurance, such as jobseekers' allowances or housing benefits.
* Family law covers marriage and divorce proceedings, the rights of children and rights to property and money in the event of separation.

Law and commerce

* Company law sprang from the law of trusts, on the principle of separating ownership of property and control.[55] The law of the modern company began with the Joint Stock Companies Act 1856, passed in the United Kingdom, which provided investors with a simple registration procedure to gain limited liability under the separate legal personality of the corporation.
* Commercial law covers complex contract and property law. The law of agency, insurance law, bills of exchange, insolvency and bankruptcy law and sales law are all important, and trace back to the mediæval Lex Mercatoria. The UK Sale of Goods Acts and the US Uniform Commercial Code are examples of codified common law commercial principles.
* Admiralty law and the Law of the Sea lay a basic framework for free trade and commerce across the world's oceans and seas, where outside of a country's zone of control. Shipping companies operate through ordinary principles of commercial law, generalised for a global market. Admiralty law also encompasses specialised issues such as salvage, maritime liens, and injuries to passengers.
* Intellectual property law aims at safeguarding creators and other producers of intellectual goods and services. These are legal rights (copyrights, trademarks, patents, and related rights) which result from intellectual activity in the industrial, literary and artistic fields.[56]
* Restitution deals with the recovery of someone else's gain, rather than compensation for one's own loss.
* Unjust enrichment is the third pillar of civil law (along with contract and tort). When someone has been unjustly enriched (or there is an "absence of basis" for a transaction) at another's expense, this event generates the right to restitution to reverse that gain.

But, law protects the rich. In other words if you have the money, you can get away with anything!

Law and regulation

The New York Stock Exchange trading floor after the Wall Street Crash of 1929, before tougher banking regulation was introduced

* Tax law involves regulations that concern value added tax, corporate tax, income tax.
* Banking law and financial regulation set minimum standards on the amounts of capital banks must hold, and rules about best practice for investment. This is to insure against the risk of economic crises, such as the Wall Street Crash of 1929.
* Regulation deals with the provision of public services and utilities. Water law is one example. Especially since privatisation became popular and took management of services away from public law, private companies doing the jobs previously controlled by government have been bound by varying degrees of social responsibility. Energy, gas, telecomms and water are regulated industries in most OECD countries.
* Competition law, known in the U.S. as antitrust law, is an evolving field that traces as far back as Roman decrees against price fixing and the English restraint of trade doctrine. Modern competition law derives from the U.S. anti-cartel and anti-monopoly statutes (the Sherman Act and Clayton Act) of the turn of the 20th century. It is used to control businesses who attempt to use their economic influence to distort market prices at the expense of consumer welfare.
* Consumer law could include anything from regulations on unfair contractual terms and clauses to directives on airline baggage insurance.
* Environmental law is increasingly important, especially in light of the Kyoto Protocol and the potential danger of climate change. Environmental protection also serves to penalise polluters within domestic legal systems.

[edit] Legal systems
Main article: Legal systems of the world

In general, legal systems can be split between civil law and common law systems.[57] The term "civil law" referring to a legal system should not be confused with "civil law" as a group of legal subjects distinct from criminal or public law. A third type of legal system—still accepted by some countries without separation of church and state—is religious law, based on scriptures. The specific system that a country is ruled by is often determined by its history, connections with other countries, or its adherence to international standards. The sources that jurisdictions adopt as authoritatively binding are the defining features of any legal system. Yet classification is a matter of form rather than substance, since similar rules often prevail.
[edit] Civil law
Main article: Civil law (legal system)
First page of the 1804 edition of the Napoleonic Code

Civil law is the legal system used in most countries around the world today. In civil law the sources recognised as authoritative are, primarily, legislation—especially codifications in constitutions or statutes passed by government—and custom.[58] Codifications date back millennia, with one early example being the Babylonian Codex Hammurabi. Modern civil law systems essentially derive from the legal practice of the Roman Empire whose texts were rediscovered in medieval Europe. Roman law in the days of the Roman Republic and Empire was heavily procedural, and lacked a professional legal class.[59] Instead a lay person, iudex, was chosen to adjudicate. Precedents were not reported, so any case law that developed was disguised and almost unrecognised.[60] Each case was to be decided afresh from the laws of the state, which mirrors the (theoretical) unimportance of judges' decisions for future cases in civil law systems today. During the 6th century AD in the Eastern Roman Empire, the Emperor Justinian I codified and consolidated the laws that had existed in Rome, so that what remained was one-twentieth of the mass of legal texts from before.[61] This became known as the Corpus Juris Civilis. As one legal historian wrote, "Justinian consciously looked back to the golden age of Roman law and aimed to restore it to the peak it had reached three centuries before."[62] Western Europe, meanwhile, slowly slipped into the Dark Ages, and it was not until the 11th century that scholars in the University of Bologna rediscovered the texts and used them to interpret their own laws.[63] Civil law codifications based closely on Roman law, alongside some influences from religious laws such as Canon law and Islamic law,[64][65] continued to spread throughout Europe until the Enlightenment; then, in the 19th century, both France, with the Code Civil, and Germany, with the Bürgerliches Gesetzbuch, modernised their legal codes. Both these codes influenced heavily not only the law systems of the countries in continental Europe (e.g. Greece), but also the Japanese and Korean legal traditions.[66][67] Today, countries that have civil law systems range from Russia and China to most of Central and Latin America.[68] The United States follows the common law system described below.
[edit] Common law and equity
Main article: Common law
King John of England signs Magna Carta

Common law and equity are legal systems where decisions by courts are explicitly acknowledged to be legal sources. The "doctrine of precedent", or stare decisis (Latin for "to stand by decisions") means that decisions by higher courts bind lower courts. Common law systems also rely on statutes, passed by the legislature, but may make less of a systematic attempt to codify their laws than in a "civil law" system. Common law originated from England and has been inherited by almost every country once tied to the British Empire (except Malta, Scotland, the U.S. state of Louisiana, and the Canadian province of Quebec). In medieval England, the Norman conquest led to a unification of various tribal customs and hence a law "common" to the whole country. Perhaps influenced by Islamic legal practices around the time of the Crusades,[69] the common law developed when the English monarchy had been weakened by the enormous cost of fighting for control over large parts of France. King John had been forced by his barons to sign a document limiting his authority to pass laws. This "great charter" or Magna Carta of 1215 also required that the King's entourage of judges hold their courts and judgments at "a certain place" rather than dispensing autocratic justice in unpredictable places about the country.[70] A concentrated and elite group of judges acquired a dominant role in law-making under this system, and compared to its European counterparts the English judiciary became highly centralised. In 1297, for instance, while the highest court in France had fifty-one judges, the English Court of Common Pleas had five.[71] This powerful and tight-knit judiciary gave rise to a rigid and inflexible system of common law.[72] As a result, as time went on, increasing numbers of citizens petitioned the King to override the common law, and on the King's behalf the Lord Chancellor gave judgment to do what was equitable in a case. From the time of Sir Thomas More, the first lawyer to be appointed as Lord Chancellor, a systematic body of equity grew up alongside the rigid common law, and developed its own Court of Chancery. At first, equity was often criticised as erratic, that it varied according to the length of the Chancellor's foot.[73] But over time it developed solid principles, especially under Lord Eldon.[74] In the 19th century the two systems were fused into one another. In developing the common law and equity, academic authors have always played an important part. William Blackstone, from around 1760, was the first scholar to describe and teach it.[75] But merely in describing, scholars who sought explanations and underlying structures slowly changed the way the law actually worked.[76]
[edit] Religious law
Main article: Religious law

Religious law is explicitly based on religious precepts. Examples include the Jewish Halakha and Islamic Sharia—both of which translate as the "path to follow"—while Christian canon law also survives in some church communities. Often the implication of religion for law is unalterability, because the word of God cannot be amended or legislated against by judges or governments. However a thorough and detailed legal system generally requires human elaboration. For instance, the Quran has some law, and it acts as a source of further law through interpretation,[77] Qiyas (reasoning by analogy), Ijma (consensus) and precedent. This is mainly contained in a body of law and jurisprudence known as Sharia and Fiqh respectively. Another example is the Torah or Old Testament, in the Pentateuch or Five Books of Moses. This contains the basic code of Jewish law, which some Israeli communities choose to use. The Halakha is a code of Jewish law which summarises some of the Talmud's interpretations. Nevertheless, Israeli law allows litigants to use religious laws only if they choose. Canon law is only in use by members of the clergy in the Roman Catholic Church, the Eastern Orthodox Church and the Anglican Communion.
A trial in the Ottoman Empire, 1879, when religious law applied under the Mecelle

Until the 18th century, Sharia law was practiced throughout the Muslim world in a non-codified form, with the Ottoman Empire's Mecelle code in the 19th century being first attempt at codifying elements of Sharia law. Since the mid-1940s, efforts have been made, in country after country, to bring Sharia law more into line with modern conditions and conceptions.[78][79] In modern times, the legal systems of many Muslim countries draw upon both civil and common law traditions as well as Islamic law and custom. The constitutions of certain Muslim states, such as Egypt and Afghanistan, recognise Islam as the religion of the state, obliging legislature to adhere to Sharia.[80] Saudi Arabia recognises Quran as its constitution, and is governed on the basis of Islamic law.[81] Iran has also witnessed a reiteration of Islamic law into its legal system after 1979.[82] During the last few decades, one of the fundamental features of the movement of Islamic resurgence has been the call to restore the Sharia, which has generated a vast amount of literature and affected world politics.[83]
[edit] Legal theory
[edit] History of law
Main article: Legal history
King Hammurabi is revealed the code of laws by the Mesopotamian sun god Shamash, also revered as the god of justice

The history of law is closely connected to the development of civilization. Ancient Egyptian law, dating as far back as 3000 BC, contained a civil code that was probably broken into twelve books. It was based on the concept of Ma'at, characterised by tradition, rhetorical speech, social equality and impartiality.[84][85] By the 22nd century BC, the ancient Sumerian ruler Ur-Nammu had formulated the first law code, which consisted of casuistic statements ("if ... then ..."). Around 1760 BC, King Hammurabi further developed Babylonian law, by codifying and inscribing it in stone. Hammurabi placed several copies of his law code throughout the kingdom of Babylon as stelae, for the entire public to see; this became known as the Codex Hammurabi. The most intact copy of these stelae was discovered in the 19th century by British Assyriologists, and has since been fully transliterated and translated into various languages, including English, German, and French.[86]

The Old Testament dates back to 1280 BC, and takes the form of moral imperatives as recommendations for a good society. The small Greek city-state, Ancient Athens, and from about 8th century BC was the first society to be based on broad inclusion of its citizenry; excluding women and the slave class. However, Athens had no legal science, and no word for "law" as an abstract concept.[87] Yet Ancient Greek law contained major constitutional innovations in the development of democracy.[88]

Roman law was heavily influenced by Greek philosophy, but its detailed rules were developed by professional jurists, and were highly sophisticated.[89][90] Over the centuries between the rise and decline of the Roman Empire, law was adapted to cope with the changing social situations, and underwent major codification during Justinian I.[91] Although it declined in significance during the Dark Ages, Roman law was rediscovered around the 11th century when mediæval legal scholars began to research Roman codes and adapt their concepts. In mediæval England, the King's judges developed a body of precedent, which later became the common law. A Europe-wide Lex Mercatoria was formed so that merchants could trade with common standards of practice; rather than with the many splintered facets of local laws. The Lex Mercatoria, a precursor to modern commercial law, emphasised the freedom of contract and alienability of property.[92] As nationalism grew in the 18th and 19th centuries, Lex Mercatoria was incorporated into countries' local law under new civil codes. The French Napoleonic Code and the German became the most influential. In contrast to English common law, which consists of enormous tomes of case law, codes in small books are easy to export and easy for judges to apply. However, today there are signs that civil and common law are converging.[93] EU law is codified in treaties, but develops through the precedent laid down by the European Court of Justice.
The Constitution of India is the longest written constitution for a country, containing 444 articles, 12 schedules, numerous amendments and 117,369 words

Islamic law and jurisprudence developed during the Middle Ages.[94] The methodology of legal precedent and reasoning by analogy (Qiyas) used in early Islamic law was similar to that of the later English common law system.[95] This was particularly the case for the Maliki school of Islamic law active in North Africa, Islamic Spain and the Emirate of Sicily. Between the 8th and 11th centuries, Maliki law developed several legal institutions that were parallel with later common law institutions.[96]

Ancient India and China represent distinct traditions of law, and have historically had independent schools of legal theory and practice. The Arthashastra, probably compiled around 100 AD (although it contains older material), and the Manusmriti (c. 100–300 AD) were foundational treatises in India, and comprise texts considered authoritative legal guidance.[97] Manu's central philosophy was tolerance and Pluralism, and was cited across Southeast Asia.[98] This Hindu tradition, along with Islamic law, was supplanted by the common law when India became part of the British Empire.[99] Malaysia, Brunei, Singapore and Hong Kong also adopted the common law. The eastern Asia legal tradition reflects a unique blend of secular and religious influences.[100] Japan was the first country to begin modernising its legal system along western lines, by importing bits of the French, but mostly the German Civil Code.[101] This partly reflected Germany's status as a rising power in the late 19th century. Similarly, traditional Chinese law gave way to westernisation towards the final years of the Ch'ing dynasty in the form of six private law codes based mainly on the Japanese model of German law.[102] Today Taiwanese law retains the closest affinity to the codifications from that period, because of the split between Chiang Kai-shek's nationalists, who fled there, and Mao Zedong's communists who won control of the mainland in 1949. The current legal infrastructure in the People's Republic of China was heavily influenced by Soviet Socialist law, which essentially inflates administrative law at the expense of private law rights.[103] Due to rapid industrialisation, today China undergoing a process of reform, at least in terms of economic, if not social and political, rights. A new contract code in 1999 represented a move away from administrative domination.[104] Furthermore, after negotiations lasting fifteen years, in 2001 China joined the World Trade Organisation.[105]
[edit] Philosophy of law
Main article: Jurisprudence
But what, after all, is a law? [...] When I say that the object of laws is always general, I mean that law considers subjects en masse and actions in the abstract, and never a particular person or action. [...] On this view, we at once see that it can no longer be asked whose business it is to make laws, since they are acts of the general will; nor whether the prince is above the law, since he is a member of the State; nor whether the law can be unjust, since no one is unjust to himself; nor how we can be both free and subject to the laws, since they are but registers of our wills.
Jean-Jacques Rousseau, The Social Contract, II, 6.[106]

The philosophy of law is commonly known as jurisprudence. Normative jurisprudence is essentially political philosophy, and asks "what should law be?", while analytic jurisprudence asks "what is law?". John Austin's utilitarian answer was that law is "commands, backed by threat of sanctions, from a sovereign, to whom people have a habit of obedience".[107] Natural lawyers on the other side, such as Jean-Jacques Rousseau, argue that law reflects essentially moral and unchangeable laws of nature. The concept of "natural law" emerged in ancient Greek philosophy concurrently and in entanglement with the notion of justice, and re-entered the mainstream of Western culture through the writings of Thomas Aquinas and the commentaries of Islamic philosopher and jurist Averroes.[108][109]

Hugo Grotius, the founder of a purely rationalistic system of natural law, argued that law arises from both a social impulse—as Aristotle had indicated—and reason.[110] Immanuel Kant believed a moral imperative requires laws "be chosen as though they should hold as universal laws of nature".[111] Jeremy Bentham and his student Austin, following David Hume, believed that this conflated the "is" and what "ought to be" problem. Bentham and Austin argued for law's positivism; that real law is entirely separate from "morality".[112] Kant was also criticised by Friedrich Nietzsche, who rejected the principle of equality, and believed that law emanates from the will to power, and cannot be labelled as "moral" or "immoral".[113][114][115]

In 1934, the Austrian philosopher Hans Kelsen continued the positivist tradition in his book the Pure Theory of Law.[116] Kelsen believed that although law is separate from morality, it is endowed with "normativity"; meaning we ought to obey it. While laws are positive "is" statements (e.g. the fine for reversing on a highway is €500); law tells us what we "should" do. Thus, each legal system can be hypothesised to have a basic norm (Grundnorm) instructing us to obey. Kelsen's major opponent, Carl Schmitt, rejected both positivism and the idea of the rule of law because he did not accept the primacy of abstract normative principles over concrete political positions and decisions.[117] Therefore, Schmitt advocated a jurisprudence of the exception (state of emergency), which denied that legal norms could encompass of all political experience.[118]
Bentham's utilitarian theories remained dominant in law until the 20th century

Later in the 20th century, H. L. A. Hart attacked Austin for his simplifications and Kelsen for his fictions in The Concept of Law.[119] Hart argued law is a system of rules, divided into primary (rules of conduct) and secondary ones (rules addressed to officials to administer primary rules). Secondary rules are further divided into rules of adjudication (to resolve legal disputes), rules of change (allowing laws to be varied) and the rule of recognition (allowing laws to be identified as valid). Two of Hart's students continued the debate: In his book Law's Empire, Ronald Dworkin attacked Hart and the positivists for their refusal to treat law as a moral issue. Dworkin argues that law is an "interpretive concept",[120] that requires judges to find the best fitting and most just solution to a legal dispute, given their constitutional traditions. Joseph Raz, on the other hand, defended the positivist outlook and criticised Hart's "soft social thesis" approach in The Authority of Law.[121] Raz argues that law is authority, identifiable purely through social sources and without reference to moral reasoning. In his view, any categorisation of rules beyond their role as authoritative instruments in mediation are best left to sociology, rather than jurisprudence.[122]
[edit] Economic analysis of law
Main article: Law and economics

In the 18th century Adam Smith presented a philosophical foundation for explaining the relationship between law and economics.[123] The discipline arose partly out of a critique of trade unions and U.S. antitrust law. The most influential proponents, such as Richard Posner and Oliver Williamson and the so-called Chicago School of economists and lawyers including Milton Friedman and Gary Becker, are generally advocates of deregulation and privatisation, and are hostile to state regulation or what they see as restrictions on the operation of free markets.[124]
Richard Posner, one of the Chicago School, runs a blog with Bank of Sweden Prize winning economist Gary Becker.[125]

The most prominent economic analyst of law is 1991 Nobel Prize winner Ronald Coase, whose first major article, The Nature of the Firm (1937), argued that the reason for the existence of firms (companies, partnerships, etc.) is the existence of transaction costs.[126] Rational individuals trade through bilateral contracts on open markets until the costs of transactions mean that using corporations to produce things is more cost-effective. His second major article, The Problem of Social Cost (1960), argued that if we lived in a world without transaction costs, people would bargain with one another to create the same allocation of resources, regardless of the way a court might rule in property disputes.[127] Coase used the example of a nuisance case named Sturges v Bridgman, where a noisy sweetmaker and a quiet doctor were neighbours and went to court to see who should have to move.[40] Coase said that regardless of whether the judge ruled that the sweetmaker had to stop using his machinery, or that the doctor had to put up with it, they could strike a mutually beneficial bargain about who moves house that reaches the same outcome of resource distribution. Only the existence of transaction costs may prevent this.[128] So the law ought to pre-empt what would happen, and be guided by the most efficient solution. The idea is that law and regulation are not as important or effective at helping people as lawyers and government planners believe.[129] Coase and others like him wanted a change of approach, to put the burden of proof for positive effects on a government that was intervening in the market, by analysing the costs of action.[130]
[edit] Sociology of law
Main article: Sociology of law

Sociology of law is a diverse field of study that examines the interaction of law with society and overlaps with jurisprudence, economic analysis of law and more specialised subjects such as criminology.[131] The institutions of social construction and legal frameworks are the relevant areas for the discipline's inquiry. At first, legal theorists were suspicious of the discipline. Kelsen attacked one of its founders, Eugen Ehrlich, who sought to make distinct the differences between positive law, which lawyers learn and apply, and other forms of 'law' or social norms that regulate everyday life, generally preventing conflicts from reaching lawyers and courts.[132][133]
Max Weber in 1917, Weber began his career as a lawyer, and is regarded as one of the founders of sociology and sociology of law,

Around 1900 Max Weber defined his "scientific" approach to law, identifying the "legal rational form" as a type of domination, not attributable to people but to abstract norms.[134] Legal rationalism was his term for a body of coherent and calculable law which formed a precondition for modern political developments and the modern bureaucratic state and developed in parallel with the growth of capitalism.[131] Another sociologist, Émile Durkheim, wrote in The Division of Labour in Society that as society becomes more complex, the body of civil law concerned primarily with restitution and compensation grows at the expense of criminal laws and penal sanctions.[135] Other notable early legal sociologists included Hugo Sinzheimer, Theodor Geiger, Georges Gurvitch and Leon Petrażycki in Europe, and William Graham Sumner in the U.S.[136][137]
[edit] Legal institutions
It is a real unity of them all in one and the same person, made by covenant of every man with every man, in such manner as if every man should say to every man: I authorise and give up my right of governing myself to this man, or to this assembly of men, on this condition; that thou givest up, thy right to him, and authorise all his actions in like manner.
Thomas Hobbes, Leviathan, XVII

Law is less a body of static rules than a "dynamic process by which rules are constantly changed, created, and molded to fit particular situations."[138] Changes are continuously made by various institutions in a society. Law's main institutions in liberal democracies are the independent judiciaries, the justice systems, the representative legislatures or parliaments, an accountable executive, a competent and non-corrupt bureaucracy, a police force, a civilian control of the military and a robust legal profession ensuring people's access to justice and a pluralistic civil society—a term used to refer to the social institutions, communities and partnerships that form law's political basis.[139][140]

John Locke, in his Two Treatises of Government, and Baron de Montesquieu in The Spirit of the Laws, advocated for a separation of powers between the political, legislature and executive bodies.[141] Their principle was that no person should be able to usurp all powers of the state, in contrast to the absolutist theory of Thomas Hobbes' Leviathan.[142] Max Weber and others reshaped thinking on the extension of state. Modern military, policing and bureaucratic power over ordinary citizens' daily lives pose special problems for accountability that earlier writers such as Locke or Montesquieu could not have foreseen. Modern international organisations tend to focus on the importance of rule of law and good governance, while other authors explore the relation of rule of law and efficient governance in modern states.[143][144]
[edit] Judiciary
Main article: Judiciary

A judiciary is a number of judges mediating disputes to determine outcome. Most countries have systems of appeal courts, answering up to a supreme legal authority. In the United States, this is the Supreme Court;[145] in Australia, the High Court; in the UK, the the Supreme Court[146] (since 1 October 2009; previously, it used to be the House of Lords);[147] in Germany, the Bundesverfassungsgericht; in France, the Cour de Cassation.[148][149] For most European countries the European Court of Justice in Luxembourg can overrule national law, when EU law is relevant. The European Court of Human Rights in Strasbourg allows citizens of the Council of Europe member states to bring cases relating to human rights issues before it.[150]
The judges of the International Court of Justice in the Hague

Some countries allow their highest judicial authority to over-rule legislation they determined as unconstitutional. In Roe v Wade, the U.S. Supreme Court overturned a Texas law which forbade the granting of assistance to women seeking abortion.[151] The U.S.'s constitution's fourteenth amendment was interpreted to give Americans a right to privacy, and thus a woman's right to choose abortion.

A judiciary is theoretically bound by the constitution, much as legislative bodies are. In most countries judges may only interpret the constitution and all other laws. But in common law countries, where matters are not constitutional, the judiciary may also create law under the doctrine of precedent. The UK, Finland and New Zealand assert the ideal of parliamentary sovereignty, whereby the unelected judiciary may not overturn law passed by a democratic legislature.[152] In communist states, such as China, the courts are often regarded as parts of the executive, or subservient to the legislature; governmental institutions and actors exert thus various forms of influence on the judiciary.[153] In Muslim countries, courts often examine whether state laws adhere to the Sharia: the Supreme Constitutional Court of Egypt may invalidate such laws,[154] and in Iran the Guardian Council ensures the compatibility of the legislation with the "criteria of Islam".[155][156]
[edit] Legislature
Main article: Legislature
The debating chamber of the European Parliament

Prominent examples of legislatures are the Houses of Parliament in London, the Congress in Washington D.C., the Bundestag in Berlin, the Duma in Moscow, the Parlamento Italiano in Rome and the Assemblée nationale in Paris. By the principle of representative government people vote for politicians to carry out their wishes. Although countries like Israel, Greece, Sweden and China are unicameral, most countries are bicameral, meaning they have two separately appointed legislative houses. In the 'lower house' politicians are elected to represent smaller constituencies. The 'upper house' is usually elected to represent states in a federal system (as in Australia, Germany or the United States) or different voting configuration in a unitary system (as in France). In the UK the upper house is appointed by the government as a house of review. One criticism of bicameral systems with two elected chambers is that the upper and lower houses may simply mirror one another. The traditional justification of bicameralism is that an upper chamber acts as a house of review. This can minimise arbitrariness and injustice in governmental action.[157]

To pass legislation, a majority of Members of Parliament must vote for a bill (proposed law) in each house. Normally there will be several readings and amendments proposed by the different political factions. If a country has an entrenched constitution, a special majority for changes to the constitution will be required, making changes to the law more difficult. A government usually leads the process, which can be formed from Members of Parliament (e.g. the UK or Germany). But in a presidential system, an executive appoints a cabinet to govern from his or her political allies whether or not they are elected (e.g. the United States or Brazil), and the legislature's role is reduced to either ratification or veto.[158]
[edit] Executive
Main article: Executive (government)
The G20 meetings are composed of representatives of each country's executive branch

The executive in a legal system serve as a government's centre of political authority. In a parliamentary system, as with Britain, Italy, Germany, India, and Japan, the executive is known as the cabinet, and composed of members of the legislature. The executive is chosen by the Prime Minister or Chancellor, whose office holds power under the confidence of the legislature. Because popular elections appoint political parties to govern, the leader of a party can change in between elections. The head of state is apart from the executive, and symbolically enacts laws and acts as representative of the nation. Examples include the German president (appointed by the Parliament); the Queen of the United Kingdom (a hereditary title), and the Austrian president (elected by popular vote). The other important model is the presidential system, found in France, the U.S. and Russia. In presidential systems, the executive acts as both head of state and head of government, and has power to appoint an unelected cabinet. Under a presidential system, the executive branch is separate from the legislature to which is not accountable.[159][160]

Although the role of the executive varies from country to country, usually it will propose the majority of legislation, and propose government agenda. In presidential systems, the executive often has the power to veto legislation. Most executives in both systems are responsible for foreign relations, the military and police, and the bureaucracy. Ministers or other officials head a country's public offices, such as a foreign ministry or interior ministry. The election of a different executive is therefore capable of revolutionising an entire country's approach to government.
[edit] Military and police
Main articles: Military and Police
U.S. Customs and Border Protection officers

While military organizations have existed as long as government itself, the idea of a standing police force is relatively modern concept. Mediæval England's system of traveling criminal courts, or assizes, used show trials and public executions to instill communities with fear to maintain control.[161] The first modern police were probably those in 17th-century Paris, in the court of Louis XIV,[162] although the Paris Prefecture of Police claim they were the world's first uniformed policemen.[163]

 

Physics formulas for grade 11, grade 12 and under graduates.
Density is mass per unit volume
Density = mass / volume
velocity = displacement / time
Force = rate of change of momentum
Momentum = mass . velocity
Power is rate of work done
Power = work / time
Unit of power is watt

Potential energy (P)
PE = m.g.h
m = mass
g = acceleration due to gravity (9.81m/s2)
h = height
Kinetic energy (P)
P = (1/2).m.v2
m = mass
v = velocity
Gravity (Force due to gravity)
Fg : Force of attraction
G : Gravitational constant
M1 : Mass of first object
M2 : Mass of second object
Fg = G M1 M2
r2

Acceleration due to gravity at a depth 'd' from earth surface is :
gd = g(1- d )
R

Acceleration due to gravity at height 'h' from earth surface is :
h is very much smaller than R
gh = g(1- 2h )
R

Escape velocity
Escape velocity from a body of mass M and radius r is

For example if you want to calculate the escape verlocity of sa object from earth then,
M is dmass of earth
r is radius of earth

OPTICS

Index of refraction
n = c/v

n - index of refraction
c - velocity of light in a vacuum
v - velocity of light in the given material

Under constant acceleration linear motion
v = final velocity
u = intitial velocity
a = acceleration
t = time taken to reach velocity v from u
s = displacement

v = u + a t

s = ut + (1/2)a t 2

s = vt - (1/2)a t 2

v2 = u2 + 2 a s
Friction force (kinetic friction)
When the object is moving then Friction is defined as :
Ff = μ Fn
where
Ff = Friction force, μ= cofficient of friction
Fn = Normal force
Linear Momentum
Momentum = mass x velocity
Capillary action
The height to which the liquid can be lifted is given by:
h = 2γcosθ
ρgr

γ: liquid-air surface tension(T)(T=energy/area)
θ: contact angle
ρ: density of liquid
g: acceleration due to gravity
r: is radius of tube

Simple harmonic motion
Simple harmonic motion is defined by:
d2x/dt2 = - k x
Time period of pendulum

Waves
f = 1
T

ω = 2 π
T

v = f . λ

where
ω = Angular frequency, T=Time period, v = Speed of wave, λ=wavelength


Doppler effect Relationship between observed frequency f and emitted frequency f0:
f = f0( v )
v + vs






where,
v=velocity of wave
vs=velocity of source. It is positive if source of wave is moving away from observer. It is negative if source of wave is moving towards observer.
Resonance of a string
frequency = f = nv
2L






where,
L: length of the string
n = 1, 2, 3...
Resonance of a open tube of air(approximate)
Approximate frequency = f = nv
2L






where,
L: length of the cylinder
n = 1, 2, 3...
v = speed of sound
Resonance of a open tube of air(accurate)
frequency = f = nv
2(L+0.8D)






where,
L: length of the cylinder
n: 1, 2, 3...
v: speed of sound
d:diameter of the resonance tube
Resonance of a closed tube of air(approximate)
Approximate frequency = f = nv
4L






where,
L: length of the cylinder
n = 1, 2, 3...
v = speed of sound
Resonance of a closed tube of air(accurate)
frequency = f = nv
4(L+0.8D)






where,
L: length of the cylinder
n: 1, 2, 3...
v: speed of sound
d:diameter of the resonance tube
intensity of sound
intensity of sound = Sound Power
area





intensity of sound in decibel= 10log10 I
I0





dB = 10log10 I
I0






where
I=intensity of interest in Wm-2
I0=intensity of interest in 10-12Wm-2

Bragg's law
nλ = 2d sinθ

where
n = integer (based upon order)
λ = wavelength
d = distance between the planes
θ = angle between the surface and the ray

de Broglie equation
λ = h = h
p mv







where
p = momentum
λ = wavelength
h = Planck's constant
v = velocity
Relation between energy and frequency
E = hν
where
E = Energy
h = Planck's constant
ν = frequency
Davisson and Germer experiment
λ = h








where
e = charge of electron
m = mass of electron
V = potential difference between the plates thru which the electron pass
λ = wavelength

Centripetal Force (F)
F = m v2 = m ω2 r
r

Circular motion formula

v = ω r
Centripetal acceleration (a) = v2
r

Torque (it measures how the force acting on the object can rotate the object)
Torque is cross product of radius and Force
Torque = (Force) X (Moment arm) X sin θ
T = F L sin θ
whete θ = angle between force and moment arm
Forces of gravitation
F = G (m1.m2)/r2
where G is constant. G = 6.67E - 11 N m2 / kg2
Stefan-Boltzmann Law
The energy radiated by a blackbody radiator per second = P
P = AσT4
where,
σ = Stefan-Boltzmann constant
σ = 5.6703 × 10-8 watt/m2K4
Efficiency of Carnot cycle
η = 1 - Tc
Th

Ideal gas law
P V = n R T
P = Pressure (Pa i.e. Pascal)
V = Volume (m3)
n = number of of gas (in moles)
R = gas constant ( 8.314472 .m3.Pa.K-1mol-1] )
T = Temperatue ( in Kelvin [K])

Boyles law (for ideal gas)
P1 V1 = P2V2
T (temperature is constant)
Charles law (for ideal gas)
V1 = V2
T1 T2

P (pressure is constant)
Translational kinetic energy K per gas molecule (average molecular kinetic energy
K = 3 k T
2

k = 1.38066 x 10-23 J/K Boltzmanns constant
Internal energy of monoatomic gas
K = 3 n R T
2

n = number of of gas (in moles)
R = gas constant ( 8.314472 .m3.Pa.K-1mol-1] )
Root mean square speed of gas
V2rms = 3 k T
m

k = 1.38066 x 10-23 J/K Boltzmanns constant
m = mass of gas
Ratio of specific heat (γ)
γ = Cp
Cv

Cp = specific heat capacity of the gas in a constant pressure process
Cv = specific heat capacity of the gas in a constant volume process
Internal entergy of ideal gas

Internal entergy of ideal gas (U) = cv nRT

In Adiabatic process no heat is gained or lost by the system.
Under adiabetic condition

PVγ = Constant
TVγ-1 = Constant
where γ is ratio of specific heat.
γ = Cp
Cv

Boltzmann constant (k)
k = R
Na

R = gas constant
Na = Avogadro's number.
Speed of the sound in gas

R = gas constant(8.314 J/mol K)
T = the absolute temperature
M = the molecular weight of the gas (kg/mol)
γ = adiabatic constant = cp/cv
Capillary action
The height to which the liquid can be lifted is given by
h=height of the liquid lifted
T=surface tension
r=radius of capillary tube
h= 2T
ρrg

Resistance of a wire
R = ρL
A







ρ = rsistivity
L = length of the wire
A = cross-sectional area of the wire
Ohm's law
V = I . R
V = voltage applied
R = Resistance
I = current

Electric power (P) = (voltage applied) x (current)
P = V . I = I2 . R
V = voltage applied
R = Resistance
I = current
Resistor combination
If resistors are in series then equivalent resistance will be
Req = R1 + R2 + R3 + . . . . . . + Rn
If resistors are in parallel then equivalent resistance will be
1/Req = 1/R1 + 1/R2 + 1/R3 + . . . . . . + 1/Rn
In AC circuit average power is :
Pavg = VrmsIrms cosφ
where,
Pavg = Average Power
Vrms = rms value of voltage
Irms = rms value of current
In AC circuit Instantaneous power is :
PInstantaneous = VmIm sinωt sin(ωt-φ)
where,
PInstantaneous = Instantaneous Power
Vm = Instantaneous voltage
Im = Instantaneous current
Capacitors
Q = C.V
where
Q = charge on the capacitor
C = capacitance of the capacitor
V = voltage applied to the capacitor
Total capacitance (Ceq) for PARALLEL Capacitor Combinations:
Ceq = C1 + C2 + C3 + . . . . . . + Cn
Total capacitance (Ceq) for SERIES Capacitor Combinations:
1/Ceq = 1/C1 + 1/C2 + 1/C3 + . . . . . . + 1/Cn
Parallel Plate Capacitor
C = κ ε0 A
d
where
C = [Farad (F)]
κ = dielectric constant
A = Area of plate
d = distance between the plate
ε0 = permittivity of free space (8.85 X 10-12 C2/N m2)
Cylindrical Capacitor
C = 2 π κ ε0 L
ln (b/a)
where
C = [Farad (F)]
κ = dielectric constant
L = length of cylinder [m]
a = outer radius of conductor [m]
b = inner radius of conductor [m]
ε0 = permittivity of free space (8.85 X 10-12 C2/N m2)
Spherical Capacitor
C = 4 π κ ε0 a b
b - a
where
C = [Farad (F)]
κ = dielectric constant
a = outer radius of conductor [m]
b = inner radius of conductor [m]
ε0 = permittivity of free space (8.85 X 10-12 C2/N m2)
Magnetic force acting on a charge q moving with velocity v
F = q v B sin θ
where
F = force acting on charge q (Newton)
q = charge (C)
v = velocity (m/sec2)
B = magnetic field
θ = angle between V (velocity) and B (magnetic field)
Force on a wire in magnetic field (B)
F = B I l sin θ
where
F = force acting on wire (Newton)
I = Current (Ampere)
l = length of wire (m)
B = magnetic field
θ = angle between I (current) and B (magnetic field)
In an RC circuit (Resistor-Capacitor), the time constant (in seconds) is:
τ = RC
R = Resistance in Ω
C = Capacitance in in farads.
In an RL circuit (Resistor-inductor ), the time constant (in seconds) is:
τ = L/R
R = Resistance in Ω
C = Inductance in henries
Self inductance of a solenoid = L = μn2LA
n = number of turns per unit length
L = length of the solenoid.


Mutual inductance of two solenoid two long thin solenoids, one wound on top of the other
M = μ0N1N2LA
N1 = total number of turns per unit length for first solenoid
N2 = number of turns per unit length for second solenoid
A = cross-sectional area
L = length of the solenoid.
Energy stored in capacitor
E = 1 C V 2
2

Coulomb's Law
Like charges repel, unlike charges attract.
F = k (q1 . q2)/r2
where k is constant. k = 1/(4 π ε0) ≈ 9 x 109 N.m2/C2
q1 = charge on one body
q2 = charge on the other body
r = distance between them

Calculator based upon Coulomb's Law

Ohm's law
V = IR
where
V = voltage
I = current
R = Resistence

Electric Field around a point charge (q)
E = k ( q/r2 )
where k is constant. k = 1/(4 π ε0) ≈ 9 x 109 N.m2/C2
q = point charge
r = distance from point charge (q)
Electric field due to thin infinite sheet
E = σ
2 ε0
where
E = Electric field (N/C)
σ = charge per unit area C/m2
ε0 = 8.85 X 10-12 C2/N m2
Electric field due to thick infinite sheet
E = σ
ε0
where

E = Electric field (N/C)
σ = charge per unit area C/m2
ε0 = 8.85 X 10-12 C2/N m2
Magnetic Field around a wire (B) when r is greater than the radius of the wire.
B = μ0 I
2 π r

where
I = current
r = distance from wire
and r ≥ Radius of the wire
Magnetic Field around a wire (B) when r is less than the radius of the wire.
B = μ0 I r
2 π R2

where
I = current
R = radius of wire
r = distance from wire
and r ≤ Radius of the wire (R)
Magnetic Field At the center of an arc
B = μ0 I φ
4 π r

where
I = current
r = radius from the center of the wire
Bohr's model
L = nh
2 π

where
L = angular momentum
n = principal quantum number = 1,2,3,...n
h = Planck's constant.
Emitting Photons(Rydberg Formula)
Ephoton = E0( 1 - 1 )
n12 n22







where
n1 < n2
E0 = 13.6 eV
Half life of radioactive element
t1/2 = ln(2)
λ

Average life of radioactive element
τ = 1
λ

 

http://hotfile.com/dl/18350516/31f2517/Taiko_no_Tatsujin.part13.rar

 

[SIGPIC][/SIGPIC]

 

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http://www.tommti-systems.de/

 

http://www.youtube.com/watch?v=6sRkPUG7aUc

 

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