Question

The electric force on a point charge situated on the axis of a short dipole is $F$. If the charge is shifted along the axis to double the distance, the electron force acting will be:

• A. $4F$
• B. $\frac{F}{2}$
• C. $\frac{F}{4}$
• D. $\frac{F}{8}$

Answer 1

The correct option is D $\frac{F}{8}$

Consider the D.M. is $P$.

Let charge $q$ is placed at the distance $r$ from the dipole.

Electric field due to the dipole at an axial point is

$E=\frac{1}{4\pi {\epsilon }_0}\frac{2p}{r^3}$

Force on a charge $q$ placed at distance $r$ is

$F=qE=\frac{1}{4\pi {\epsilon }_0}\frac{2pq}{r^3}$

If we doubled the distance

$F^{\prime }=\frac{1}{4\pi {\epsilon }_0}\frac{2pq}{{\left(2r\right)}^3}$

$F^{\prime }=\frac{1}{4\pi {\epsilon }_0}\frac{2pq}{r^3}\left(\frac{1}{8}\right)$

$F^{\prime }=\frac{F}{8}$

Hence,option $D$ is the correct answer.