Question

A solid metallic sphere has a charge . Concentric with this sphere is a conducting spherical shell having charge . The radius of the sphere + 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. $\frac{Q}{2\pi {ϵ}_{0}R}$
• B. $\frac{3Q}{2\pi {ϵ}_{0}R}$
• C. $\frac{3Q}{4\pi {ϵ}_0{R}^2}$
• D. $\frac{4Q}{4\pi {ϵ}_0{R}^2}$

Answer 1

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

Electric field at a distance R is only due to sphere because electric field due to shell inside it is always zero. Hence electric field $=\frac{1}{4\pi {ϵ}_0}.\frac{3Q}{R^2}$