### Important Scientific Laws

## Avogadro’s Law

It states that equal volumes of all gases under the same conditions of temperature and pressure contain equal number of molecules. This means that as long as the temperature and pressure remain constant, the volume (V) depends upon number of molecules of the gas or in other words amount of the gas. Mathematically we can write V ∝ n [where n is the number of moles of the gas.] ⇒ V = k n [k is the proportionality constant] The number of molecules in one mole of a gas has been determined to be 6.022 ×1023 and is known as Avogadro constant.

## Boyle’s Law

At constant temperature, the pressure of a fixed amount (i.e., number of moles n) of gas varies inversely with its volume. This is known as Boyle’s law. Mathematically, it can be written as p ∝ 1/V ( at constant T and n) p =k *(1/V) where k is the proportionality constant. The value of constant k depends upon the amount of the gas, temperature of the gas and the units in which p and V are expressed.

## Charles’ Law

States that pressure remaining constant, the volume of a fixed mass of a gas is directly proportional to its absolute temperature. V = k T The value of constant k is determined by the pressure of the gas, its amount and the units in which volume V is expressed. The above equation is the mathematical expression for Charles’s law

## Coulomb’s Law

Coulomb’s law is a quantitative statement about the force between two point charges. Coulomb’s Law states that the force between two point charges varied inversely as the square of the distance between the charges and was directly proportional to the product of the magnitude of the two charges and acted along the line joining the two charges. Thus, if two point charges Q1, Q2 are separated by a distance r in vacuum, the magnitude of the force (F) between them. Mathematically is given by: F=k [Q 1 Q2]/r2

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**Faraday’s Law of Electromagnetic Induction**

The magnitude of the induced e.m.f in a circuit is equal to the time rate of change of magnetic flux through the circuit. Or, in other words, the induced e.m.f in a wire loop is proportional to the rate of change of magnetic flux through the loop. ε = – d Φ B / d t where, magnetic flux= Φ B and ε is the induced e.m.f. The minus sign in Faraday’s Law gives the direction of the induced e.m.f.

## Hooke’s Law

Stress and strain take different forms in the situations .For small deformations the stress and strain are proportional to each other. This is known as Hooke’s law. Thus, stress ∝ strain stress = k × strain where k is the proportionality constant and is known as modulus of elasticity. Hooke’s law is an empirical law and is found to be valid for most materials. However, there are some materials which do not exhibit this linear relationship.

## Joule’s Law

It states that, heat produced by an electric current is directly proportional to the resistance of the conductor, the square of the current, and the time for which it flows. Joule’s law implies that the heat produced is: (i) Directly proportional to the square of the current (I) for a given Resistance.(R) (ii) Directly proportional to resistance R for a given current (I) (iii) Directly proportional to the time of passage of current. (iv) The heat produced is inversely proportional to resistance R for a given V (potential)

## Kepler’s laws of planetary motion

- Law of Orbits: All planets move in elliptical orbits with the Sun situated at one of the foci of the ellipse.
- Law of Areas: The line that joins any planet to the sun sweeps equal areas in equal intervals of time. This law comes from the observations that planets appear to move slower when they are farther from the sun than when they are nearer.
- Law of Periods: The Square of the time period of revolution of a planet is proportional to the cube of the semi-major axis of the ellipse traced out by the planet.

## Lambert-Beer’s Law

The law states that there is a logarithmic dependence between the transmission (or transmittance), T, of light through a substance and the product of the absorption coefficient of the substance, α, and the distance the light travels through the material (i.e., the path length), ℓ.

## Lenz’s Law

In 1834, German physicist Heinrich Friedrich Lenz (1804-1865) deduced a rule, known as Lenz’s law which gives the polarity of the induced e.m.f in a clear and concise fashion. The statement of the law is: The polarity of induced e.m.f is such that it tends to produce a current which opposes the change in magnetic flux that produced it. In other words, A current produced by an induced e.m.f moves in a direction so that the magnetic field it produces tends to restore the changed magnetic flux.

## Newton’s Law of motion

**Newton’s First Law of Motion**: Any object remains in the state of rest or in uniform motion along a straight line, until it is compelled to change the state by applying external force. Explanation: If any object is in the state of rest, then it will remain in rest until an external force is applied to change its state. Similarly an object will remain in motion until any external force is applied over it to change its state. For example: A person standing in a bus falls backward when bus is start moving suddenly. This happens because the person and bus both are in rest while bus is not moving, but as the bus starts moving the legs of the person start moving along with bus but rest portion of his body has tendency to remain in rest.

**Newton’s Second Law of Motion**– The rate of change of momentum is directly proportional to the force applied in the direction of force. For example; when acceleration is applied on a moving vehicle, the momentum of the vehicle increases and the increase is in the direction of motion because the force is being applied in the direction of motion. On the other hand, when brake is applied on the moving vehicle, the momentum of the vehicle decreases and the decrease is in the opposite direction of motion because the force is being applied in the opposite direction of motion.

**Newton’s Third Law of Motion**– There is an equal and opposite reaction for every action Explanation: Whenever a force is applied over a body, that body also applies same force of equal magnitude and in opposite direction. For example: Walking of a person. During walking, a person pushes the ground in backward direction and in the reaction the ground also pushes the person with equal magnitude of force but in opposite direction. This enables him to move in forward direction against the push.

## Ohm’s Law

Basic law regarding flow of currents was discovered by G.S. Ohm in 1828. If a current ‘I’ is flowing through a conductor and let V be the potential difference between the ends of the conductor; Then Ohm’s law states that V ∝ I or, V = R I where the constant of proportionality R is called the resistance of the conductor. This is the Ohm’s Law. The SI unit of resistance is

**ohm**and is denoted by the symbol**Ω.**##
**Snell’s Law**

When a beam of light encounters another transparent medium, a part of light gets reflected back into the first medium (1) while the rest enters the other (2). The ratio of the sine of the angle of incidence to the sine of angle of refraction is constant. We have, (Sin i/ Sin r) = n21Where, the angles of incidence (i ) and refraction (r ) are the angles that the incident and its refracted ray make with the normal respectively and n21 is a constant, called the

*refractive index*of the second medium with respect to the first medium. This equation is called Snell’s Law of Refraction of Light.
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