Question

The electrostatic force between two point charges is directly proportional to the
(A) Sum of the charges
(B) Distance between the charges
(C) Permittivity of the medium
(D) Square of the distance between the charges
(E) Product of the charges

Answer 1

Hint
The relation between the amount of the charge, distance between the charges and the electrostatic force between two charges are best described in Coulomb's law. According to Coulomb's law, the electrostatic force between two point charges depends on the product of the charges and the separation between them.

Complete step by step answer
Coulomb’s law of electrostatics states that, when two charges q1 and q2 are separated by a distance r, the electrostatic force between the charges is directly proportional to the product of the charges, and inversely proportional to the square of the distance between them.
When we put the statement as relation,
$\Rightarrow F \propto {q_1}{q_2}$
And,
$\Rightarrow F \propto \dfrac{1}{{{r^2}}}$
When we introduce a constant of proportionality K, we get,
$\Rightarrow F = \dfrac{{K{q_1}{q_2}}}{{{r^2}}}$
Where, K is a constant and is calculated by,
$\Rightarrow K = \dfrac{1}{{4\pi {\varepsilon _0}}}$
Where $ε_0$ is the permittivity of free space.
Thus, the electrostatic force between two point charges is directly proportional to the product of the two charges.
Hence, the correct option is (E).

Note
The electrostatic force may be attractive or repulsive, depending upon the sign of the two charges.
- If both the charges are positive or negative, the electrostatic force is repulsive. The force is positive in this case.
- If one of the charges is positive, and the other one is negative, the electrostatic force is attractive. The force is negative in this case.
The Coulomb's law is only applicable for point and static charges. It is because,
- When it comes to two bodies, the charge is not uniform and we cannot take a single point to determine the distance.
- When it comes to moving charges, there is a current produced because of movement. It also produces magnetic fields, in turn, we cannot consider the Coulomb's law alone.