Question

State and explain Coulomb’s law of electric charges in scalar form.

Answer 1

Recall the statement for Coulomb's law of electric charges. Using this statement, derives the mathematical equation for the electrostatic force of attraction or repulsion between the two charges. Explain all the terms used in the mathematical equation.

Complete step by step solution:
The statement of Coulomb’s law of electric charges is as follows:
“The electrostatic force of attraction or repulsion between any two point charges is directly proportional to the product of the two charges and inversely proportional to the square of distance between the charges.”
If ${q_1}$ and ${q_2}$ are two charges and $r$ is the distance between these charges then the electrostatic force $F$ of attraction or repulsion between these two charges is
$F \propto \dfrac{{{q_1}{q_2}}}{{{r^2}}}$
$\Rightarrow F = \dfrac{1}{{4\pi {\varepsilon _0}}}\dfrac{{{q_1}{q_2}}}{{{r^2}}}$
Here, $\dfrac{1}{{4\pi {\varepsilon _0}}}$ is the constant of proportionality and ${\varepsilon _0}$ is the permittivity of the free space.
The value of the constant of proportionality $\dfrac{1}{{4\pi {\varepsilon _0}}}$ is $9 \times {10^9}\,{\text{N}} \cdot {{\text{m}}^2}/{{\text{C}}^2}$.
The force of electrostatic force of attraction or repulsion between the two charges is along the line joining the two charges.

Additional Information:
Coulomb's law is used to determine the force and distance between the two charges. One can also determine the electric field using the force obtained from Coulomb’s law.
There are also some demerits of Coulomb’s law as follows:
1. This law is applicable only when the inverse square law is obeyed.
2. This law is not applicable for large bodies.
3. This law does not hold good for bodies with irregular shape because for such bodies it becomes difficult to determine the distance between them.

Note:
The students should always keep in mind that Coulomb’s law of electric charges is only applicable to the very small bodies as we have stated in the statement for Coulomb’s law of electric charges that the force of electrostatic attraction or repulsion is only between the point charges.