Question

State Coulomb's law, explain its vector form and define S.I. unit of electric charge. State the two limitations of Coulomb's law.

Answer 1

Hint: In this, we first get the relation between the force, the charges and distance between the charges. Then further, we will give the vector form of coulomb law. Understanding of the basic concepts of coulomb’s law will help us find its limitations.

Formula used:
$F = \dfrac{1}{{4\pi \varepsilon {}_0}}\dfrac{{{q_1}{q_2}}}{{r_{}^{^2}}}$

Complete step-by-step answer:
Coulomb's law is defined as the force of attraction or repulsion between two charged bodies which is directly proportional to the product of their charges and inversely proportional to the square of the distance between them. It acts along the line joining the two charges considered to be point charges.
$F = \dfrac{1}{{4\pi \varepsilon {}_0}}\dfrac{{{q_1}{q_2}}}{{r_{}^{^2}}}$
Vector form of coulomb’s law is given by:
$\eqalign{
  & {{\vec F}_{12}} = \dfrac{1}{{4\pi \varepsilon {}_0}}\dfrac{{{q_1}{q_2}}}{{r_{_{12}}^{^2}}}{{\overset{\lower0.5em\hbox{$\smash{\scriptscriptstyle\frown}$}}\to
 {r} }_{12}}.........(1) \cr
& {{\vec F}_{12}} = - {{\vec F}_{21}}...............(2) \cr} $
In the above equation, ${F_{12}}$ is the force exerted by ${q_1}$ on ${q_2}$ and ${F_{21}}$ is the force exerted by ${q_2}$ on ${q_1}$
Also, the second equation tells us that Coulomb's law holds for stationary charges only which are point sized and this law obeys Newton’s third law.
Now, since we know that an electric charge is the physical property of matter that causes it to experience a force when placed in an electromagnetic field.
The S.I unit of electric charge is coulomb represented by C. Coulomb is defined as an ampere second.
There are some limitations of this law as following:
1. This law is applicable only for the point charges at rest.
2. Coulomb’s Law can only be applied in the cases where the inverse square law is obeyed.
3. It is also difficult to implement Coulomb’s law where charges are in arbitrary shape because in such cases we cannot determine the distance between the two charges.
4. This law cannot be used directly to calculate the charge of the big planets.

Additional Information: We know that there are two types of electric charge namely positive charges and negative charges. Same charges repel each other whereas unlike charges attract each other.

Note: The coulomb’s law is only valid for point charges which are at rest. Force is an extensive property, also mass is an extensive property, as it depends on the number of particles. We should also notice that the product of an extensive property and an intensive property will give us extensive property as a result.