Explaination Of Columb's Law For A-Level Students

Coulomb's Law:-
Coulomb's law:-This law was given by a French scientist Charles Augustine de Coulomb in 1875 A.D.

History:-Coulomb performed a number of experiments to measure the force between two electric charges.The apparatus used by coulomb was known as Torsion Balance.Coulomb stated his experimental observations in the form of a statement known as Coulomb law.

Statement:-This law states that the magnitude of electrostatic force between two stationary point charges is directly proportional to the product of the magnitudes of the charges and is inversely proportional to the square of the distance between them and this force acts along the line joining the charges.

Mathematical form:-Let us suppose there are two electric point charges q1 ­and q2 separated by a distance r, and then electrostatic force Fe between the charges according to Coulomb law is given as

Fe = k q1q2

r2

Vector Form of Coulomb's law:-Let r^ is the unit vector in the direction of the force, then force in vector form is given as

Fe = F . r^ ……… 1

Where Fe = k q1q2

r2

Putting this value of Fe in equation 1, we get

Fe = k q1q2 . r ^

r2

This equation gives vector form of coulomb's law.

Where Fe is the electrostatic force, k is the constant of proportionality, q1 and q2 are charges, r is the distance between charges and r^ is the unit vector along a line joining the two charges.

Derivation of mathematical form:-

According to the definition of Coulomb law, we know that

Fe ∞ q1q2 ………. 1

And

Fe ∞ 1 / r2 …………. 2

Now combining 1 and 2 we get,

Fe ∞ q1q2 / r2

Replacing proportionality sign with constant of proportionality, we get,

Fe = k q1q2 / r 2

This equation gives mathematical form of Coulomb law.

In vector form is written as

Fe = k q1q2. r^

r 2

where r^ is the unit vector along the line joining the charges.If q1 is considered the source charge, then the force is positive and directed from q1 to q2 ­ and if q2 is considered as source charge, then force is negative and directed from q2 to q1.

Explanation:-As we know that force is a vector quantity, therefore, we will explain coulomb's force or law in to two parts:-

Magnitude of force:-The magnitude of coulomb's force depends on two factors:-

v Depends directly on the product of the magnitude of charges

F ∞ q1 x q2

This means that if we make q1 or q2 double, the force will become double. And if we make both of them double, the force will increase four times.

v Depends inversely on the square of the distance between the two charges.

F ∞ 1 / r2

This means that if we double the distance, the force will become one fourth and if we half the distance, the force will increase four times.

Direction of force:-In electrostatic, a charge that is exerting a force is called a source charge. And a charge on which a force is exerted is called a field charge. The direction of force is determined with respect to the source charge. To explain this, let us consider an example of tow similar charges (either both are positive and both negative) below. If q1 is considered as a source charge, then the direction of force (r^) is directed from q1 to q2, and if q 2 is considered as source charge, then the direction of force is from q2 to q1.

In the second case, force is attractive. If q1 is considered source charge, then force is directed towards it and if q2­ is considered source charge, then force is directed towards q2.

There is a convention that a repulsive force is represented by +ive and an attractive force is represented by –ive sign. For like charges, the product q1q2 is positive. This means that the force is repulsive. In such a case, the force is directed away from the source. For unlike charges, the product q1q2 is negative. This means that the force is attractive and the force is directed towards the source charge.

Constant of proportionality K-The constant of proportionality K depends on system of units used and the properties of the medium around the charges. In SI units and free space and for our easiness, we write the constant K as

K = 1 / 4 π εo N m 2 / C2

The constant εo is called the permittivity of free space. Its value is measured experimentally and is found to be εo = 8.85418 x 10-12 C2 / N . m2

If we put, this value of εo, we get K = 9 x 109 N m2 / C2

In SI units, and for charges placed in vacuum (or free space), coulombs law in equation 1 can be written as

F = 1 / 4 π εo. q1q2 / r2 . r^ ……….. 1