Question

A spherical cavity of radius \(\dfrac{R}{2}\) is made in a sphere of radius \(R\) of uniform volume charge density \(\rho\). The electric field at point \(P\) inside the cavity is

• A. $\frac{\rho R}{6{\epsilon }_0}\hat{i}$
• B. $\frac{\rho R}{3{\epsilon }_0}\hat{j}$
• C. $\frac{\rho R}{3{\epsilon }_0}[\sin \theta \hat{i}+\cos \theta \hat{j}]$
• D. $\frac{\rho R}{6{\epsilon }_0}[\sin \theta \hat{i}+\cos \theta \hat{j}]$

Answer 1

The correct option is A $\frac{\rho R}{6{\epsilon }_0}\hat{i}$

${\overrightarrow{E}}_{\rho }=\overrightarrow{E}$ at center of cavity
$=\frac{\rho }{3{\epsilon }_0}\left(\frac{R}{2}\right)\hat{i}=\frac{\rho R}{6{\epsilon }_0}\hat{i}$