Question

The magnitude of electric field intensity at a distance 'd' from a charge q is E. An identical charge is placed at a distance '3d' from it. Then, the magnitude of force it experiences is?

• A. $\frac{qE}{4}$
• B. $\frac{qE}{9}$
• C. $\frac{qE}{3}$
• D. $\frac{qE}{2}$

Answer 1

The correct option is B $\frac{qE}{9}$

The electric field intensity at a distance d from point charges is
$E=\frac{1}{4\pi {\epsilon }_0}\cdot \frac{q}{d^2}$
Intensity at a distance $3d$ is
$E^{\prime }=\frac{1}{4\pi {\epsilon }_0}\cdot \frac{q}{(3d{)}^2}$
$\therefore \frac{E}{E^{\prime }}=\frac{9}{1}$
$\therefore E^{\prime }=\frac{E}{9}$.
Hence, the magnitude electrostatic force on charge q at a distance $3d$ is
$F=q{E}^{\prime }=\frac{qE}{9}$.