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

Explanation

Important aspects of Coulomb.s law :
(i) It gives an ida about the force between two point charges the electrostatic force is directly proportional to the product of the magnitude of the two point charges and is inversely proportional to the square of the distance between the two point charges `Fprop(q_(1)q_(2))/(r^(2))`.
(ii) The force on the charge `q_(2)` exerted by the charge q1 always lies along the line joining the two charges. `r_(12)` is the unit vector pointing from charge `q_(1)` to `q_(2)` . Conversely, the force on the charge `q_(1)` exerted by `q_(2)` is along `-hatr_(12)` (i.e., in the direction opposite to `hatr_(12)`.
(iii) `k=(1)/(4piepsi_(0))` and its value is `k=9xx10^(9)Nm^(2)C^(-2)` Here `epsi_(0)` is the permittivity of free space or vacuum an the value of `(1)/(4pik)=8.85xx10^(-12)C^(2)N^(-1)m^(-2)`
(iv) The magnitude of the electrostatic force between two charges each of one coulomb and separated by a distance of 1 m is `9xx10^(9)N`
`vec(F)_(21)=(1)/(4piepsi_(0))(q_(1)q_(2))/(r^(2))hatr_(12)`
(v) Coulomb.s law in vacuum takes the form `vec(F)_(21)=(1)/(4piepsi_(0))(q_(1)q_(2))/(r^(2))hatr_(12)`. In a medium of permitivity `epsi` the force between two point charges is given by `vec(F)_(21)=(1)/(4piepsi_(0))(q_(1)q_(2))/(r^(2))hatr_(12)`
(vi) Since `epsigtepsi_(0)`, the force between two point charges in a medium other than vacuum is always less than that in vacuum. The relative permittivity for a given medium as `epsi_(r)=(epsi)/(epsi_(0))`
For vacuum or air, `epsi_(r)=1` and for all other media `epsi_(r)gt1`.
(i) Coulomb.s law has same structure as Newton.s law of gravitation.
(ii) It helps to specify the direction of electirc field due to charges.
(iii) The force on a charge `q_(1)` exerted by a point charge `q_(2)` is given by `vec(F)_(12)=(1)/(4piepsi_(0))(q_(1)q_(2))/(r^(2))hatr_(21)`
Here `epsi_(0)` is the unit vector from charge `q_(2)` to `q_(1)`.
But `hatr_(21)=-hatr_(12)`
`vec(F)_(12)=(1)/(4piepsi_(0))(q_(1)q_(2))/(r^(2))(-hatr_(12))=-(1)/(4piepsi_(0))(q_(1)q_(2))/(r^(2))(-hatr_(12))(or)vec(F)_(12)=-vec(F)_(21)`
Therefore, the electrostatic force obeys Newton.s third law.
(vii) The expression for Coulomb force is true only of point charges. However we can aaply Coulomb.s law for two charged objects whose sizes are very much smaller than the distance between them. In fact, Coulomb discovered his law by considering the charged spheres in the torsion balance as point charges. The distance between the two charged spheres is much greater than the radii of the spheres.