A point charge is placed at any point on the axis of an electric dipole at some large distance, experiences a force F. The force acting on the point charge when its distance from the dipole is halved will be
Answer & explanation
Correct answer: option 2
The correct answer is Option (2) → \( 8F \)
The force on the point charge is \( F = qE \), where \( E \) is the field of the dipole on its axis. At a large distance \( r \) (much greater than the dipole length) this field falls as the inverse cube of the distance:
\( \displaystyle E_{\mathrm{axial}} = \frac{1}{4\pi\varepsilon_0}\,\frac{2p}{r^{3}} \;\Rightarrow\; F \propto \frac{1}{r^{3}} \)
Halving the distance:
\( \displaystyle \frac{F'}{F} = \left(\frac{r}{r/2}\right)^{3} = 2^{3} = 8 \;\Rightarrow\; F' = 8F \)