# 2 charges, q_A and q_B are separated by distance, r, and exert a force, F, on each other. What new force will exist if: a) q_A is doubled? b) q_A and q_B are cut in half? c) r is a 1/3 of its normal value? d) r is cut in half, q_A is doubled?

## and e) ${q}_{A}$ is doubled and r is doubled?

Jun 25, 2018

#### Explanation:

The force is directly proportional to the product of charges i.e. ${q}_{A} {q}_{B}$ and is inversely proportional to the square of the distance ($r$) between them. Hence,

(a) As one of the charges is doubled, their product too is doubled and force is doubled.

(b) if both charges are halved, their product will become one-fourth and force too will become one fourth.

(c) if $r$ is $\frac{1}{3}$ of its normal value, force will become $9$ times its original value.

(d) if $r$ is cut to half, force becomes four times. But doubling ${q}_{A}$ also doubles product of charges and on net basis force becomes eight times.