Question

Two small objects each with a net charge of +Q exert a force of magnitude F on each other. We replace one of the objects with another whose net charge is + 4Q. We move the +Q and +4Q charges to be 3 times as far apart as they were. What is the magnitude of the force on the +4Q charge ?

• A. F
• B. 4F
• C. 4F/3
• D. 4F/9
• E. F/3

Answer 1

The correct option is D 4F/9

Initially

$q_1=q_2=Q$ and $r=R$

Force was $F=\frac{q_1{q}_2}{4\pi {ϵ}_o{r}^2}=\frac{Q^2}{4\pi {ϵ}_o{R}^2}$

Thenafter:-

$q_1=Q,q_2=4Q$ and $r=3R$

Force on charge 4Q, $F^{\prime }=\frac{Q.4Q}{4\pi {ϵ}_o(3R{)}^2}=\frac{4Q^2}{4\pi {ϵ}_o\left(9R^2\right)}$

$⟹F^{\prime }=\frac{4}{9}F$

Answer-(D)