Question

A solid metallic sphere has a change $+3Q$. 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

The correct option is B $\frac{3Q}{4\pi {\epsilon }_0{R}^2}$

Charge $=+3Q$

Change having $=-Q$

radius of sphere $=a$ $(b>a)$

Electric field at a distance $=R$ $(a<R<b)$ from the centre.

When electric field inside shell is always zero. Hence, the electric field intensity due to solid sphere is alone considered and at a distance ${}^{\prime }{R}^{\prime }$ from its centre.

Now, $E=\frac{1}{4\pi {ϵ}_0}\frac{\left(3Q\right)}{R^2}$