Question

Consider the electric force between a pair of charged particles a certain distance apart. By Coulomb's Law: If instead, the distance between the particles is doubled, the force becomes _____.

a. one fourth.
b. half.
c. double.
d. 4 times.

Answer 1

Answer:

$F'=\dfrac{1}{4}\times F$

Explanation:

The electric force between two charged particle is given by :

$F=k\dfrac{q_1q_2}{d^2}$

d is the distance between charged particles

Let F' is the force when the distance between the particles is doubled, d' = 2d

New force is given by :

$F'=k\dfrac{q_1q_2}{(d')^2}$

$F'=k\dfrac{q_1q_2}{(2d)^2}$

$F'=\dfrac{1}{4}\times k\dfrac{q_1q_2}{(d)^2}$

$F'=\dfrac{1}{4}\times F$

The new force becomes one fourth of the original force. So, if the distance between the particles is doubled, the force becomes one fourth.