Question

Two charged objects separated by some distance attract each other. If the charges on both objects are doubled with no change in distance between them, what happens to the magnitude of the force between the objects?
a. the force between them quadruples
b. the between them doubles
c. the between them is halved
d. the force between them is quartered
e. the force between them is unchanged

Answer 1

Answer:

a. the force between them quadruples

Explanation:

The electrostatic force between two charges is given by

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

where

k is the Coulomb's constant

q1 and q2 are the two charges

r is the separation between the two charges

In this problem, the charges on both objects are doubled, so

$q_1' = 2q_1\\q_2' = 2q_2$

While the distance does not change, so the new force will be

$F'= k \frac{(2q_1)(2q_2)}{r^2}=4 (k\frac{q_1 q_2}{r^2})=4 F$

so, the force will quadruple.