Question

A solid metallic sphere has a charge $+3 Q$. 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 \,{{\varepsilon }_{0}}{{R}^{2}}} $
• B. $ \frac{3Q}{4\pi \,{{\varepsilon }_{0}}{{R}^{2}}} $
• C. $ \frac{3Q}{2\pi \,{{\varepsilon }_{0}}{{R}^{2}}} $
• D. $ \frac{Q}{2\pi \,{{\varepsilon }_{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
$E=\frac{1}{4 \pi \varepsilon_{0}} \frac{q}{R^{2}}$
Given, $q=+3 Q$
Therefore, $E=\frac{1}{4 \pi \varepsilon_{0}} \frac{3 Q}{R^{2}}$