Question

When two point charges are a distance d part, the electric force that each one feels from the other has magnitude F. In order to make this force twice as strong, the distance would have to be changed to d/?2. Could you explain why?

Answer 1

Answer:

Because the force is inversely proportional to the square of the distance

Explanation:

The magnitude of the electrostatic force between two charged particles is given by

$F=k\frac{q_1 q_2}{d^2}$

where

k is the Coulomb's constant

q1, q2 are the magnitudes of the two charges

d is the distance between the two charges

We observe that the magnitude of the force is inversely proportional to the square of the distance.

Therefore, when the distance changes to

$d'=\frac{d}{\sqrt{2}}$

The force will double:

$F'=k\frac{q_1 q_2}{(d/\sqrt{2})^2}=2(k\frac{q_1 q_2}{d^2})=2F$