Question

A solid metallic sphere has a charge $+3Q$. Concentric with this sphere is a conducting spherical shell having charge $-Q$. The radius of the sphere is $a$ and that of the spherical shell is $b(b>a)$. What is the electric field at a distance $R(a<R<b)$ from the centre ?

• A. $\frac{4Q}{2\pi {\epsilon }_0{R}^2}$
• B. $\frac{3Q}{4\pi {\epsilon }_0{R}^2}$
• C. $\frac{3Q}{2\pi {\epsilon }_0{R}^2}$
• D. $\frac{Q}{2\pi {\epsilon }_{0}R}$

Answer 1

Answer: (B)

The electric field inside a spherical charge is everywhere zero, that is
$E=0$
But point $P$ is outside the inner sphere, hence for a point very close to the surface the intensity of electric field is given by
$E=\frac{1}{4\pi {\epsilon }_0}\frac{q}{R^2}$
Given, $q=+3Q$
Therefore, $E=\frac{1}{4\pi {\epsilon }_0}\frac{3Q}{R^2}$