Question

A short electric dipole moment $\overrightarrow{p}$ is placed at a distance $r$ from the centre of a solid metallic sphere of radius $a(<<r)$ as shown in the figure. The electric field intensity at the centre of sphere $C$ due to induced charge on the sphere is :

• A. zero
• B. $\frac{1}{4{\pi \epsilon }_0}\frac{2p}{r^3}$ along $CO$
• C. $\frac{1}{4{\pi \epsilon }_0}\frac{2p}{r^3}$ along $OC$
• D. $\frac{1}{4{\pi \epsilon }_0}\frac{p}{r^3}$ along $CO$

Answer 1

Answer: (B)

Electric field at $C$ due to electric dipole
$=\frac{1}{4\pi {\epsilon }_0}\frac{2p}{r^3}$ along $OC$
Electric field at $C$ due to induced charge must be equal and opposite to electric field due to dipole as net field at $C$ is zero.