Explain in detail Coulomb 's law and its various aspects.

Explanation

Consider two point charges `q_1 and q_2` at rest in vaccum, and separated by a distance of r. According to coloumb, the force on the point charge `q_2` exerted by another point charge `q_1` is
`vecF_(21) = k(q_1q_2)/r^2 hatr_(12)`
where `hatr_(12)` is the unit vector directed from charge `q_1` to charge `q_2` and k is the proportionally constant .
Important aspects of Coulomb.s law:
(i) Coulomb.s law states that the electrostatic force is directly proportional to the product of the magnitude of the two point charges anf is inversely proportional to the square of the distance between the two point charges.
(ii) The force on the charge `q_2` excerted by the charge `q_1` always lies alnong the line joiniing the two charges. `hatr_(12)` is the unit vector pointing from charge `q_1` to q_2`. Conversely, the force on the charge `q_1` excerted by `q_2` is alng - `hatr_(12)` (i.e., in the direction oppposite to `hatr_(12)`).
(iii) In SI units, `k = 1/(4piepsilon_0)` and its value is `k = 9 xx 10^9 Nm^2C^-2`. Here `epsilon_0` is the permitively of free space or vaccum and the value of
`epsilon_0 = 1/(4pik)`
`= 8.85 xx 10^-12C^2N^-1m^-2`.
(iv) The magnitude of the elcectrostatic force between two charges each of one coulomb and separated by a disatance of 1 m is calcualted as follows:
`|F| = (9 xx 10^9 xx 1 xx 1)/1^2 = 9 xx 10^9 N`
(v) The reltive permitivity for a given medium is defined as
`epsilon_r = epsilon/epsilon_0`
For vaccum on air, `epsilon_r = 1` and for all other media `epsilon_r gt 1`.
(vi) Coulomb.s law has same structure as Newton.s law of gravitation. Both are inversely proportional to the squre of the distance between the particles. The electrostatic forces is directly proportional to the product of the magnitutde of two point charges and gravitaional force is directly proportional to the product of two masses.