Question

For distance far away from centre of dipole the change in magnitude of electric field with change in distance from the centre of dipole is

• A. zero.
• B. same in equatorial plane as well as axis of dipole.
• C. more in case of equatorial plane of dipole as compared to axis of dipole.
• D. more in case of axis of dipole as compared to equatorial plane of dipole.

Answer 1

Answer: (D)

For distances far away from centre of dipole
$E_{axis}=E_a=\frac{1}{4\pi {\epsilon }_0}\frac{2p}{r^3}$
$E_{\text{equa }}=E_e=\frac{1}{4\pi {\epsilon }_0}-\frac{p}{r^3}$
$\frac{d}{dr}\left(E_a\right)=\frac{1}{4\pi {\epsilon }_0}2p\frac{d}{dr}\left(r^{-3}\right)=-6\cdot \frac{1}{4\pi {\epsilon }_0}\frac{p}{r^4}$.....(i)
$\frac{d}{dr}\left(E_c\right)=\frac{1}{4\pi {\epsilon }_0}p\frac{d}{dr}\left(r^{-3}\right)=-3\frac{1}{4\pi {\epsilon }_0}\frac{p}{r^4}$....(ii)
From equations (i) and (ii) the magnitude of change in electric field w.r.t. distance is more in case of axis of dipole as compared to equatorial plane.