Question

In the situation shown in the figure, we have three concentric metallic shells. The inner and outer shells are earthed, but the middle shell is given charge $+Q$. Comment on the electric field in the different regions.

• A. Electric field in region III is zero.
• B. Electric field in region II is outwards.
• C. Electric field in region I is zero.
• D. Electric field in region I is inwards.

Answer 1

Answer: (A), (B), (D)

Electric field in region I is inwards.

Let us suppose $+q$ charge appears on the innermost shell.

So, the possible charge distribution is shown in the figure.


Potential of the innermost shell should be zero as it is earthed.

$\therefore \frac{kq}{a}-\frac{kq}{b}+\frac{k(Q+q)}{b}-\frac{k(Q+q)}{c}=0$

$\Rightarrow q(\frac{1}{a}-\frac{1}{c})=Q(\frac{1}{c}-\frac{1}{b})$

$\Rightarrow q=\frac{\frac{Q(b-c)}{bc}}{\frac{(c-a)}{ac}}=\frac{Qa(b-c)}{b(c-a)}=-ve\because b<c$

and $q<Q$.

Therefore, the charge appearing on the innermost shell should be $-q$.

The charge distribution is shown in the figure.


Hence, in region I, the electric field is radially inwards and in region II is radially outwards.

The outermost shell act as shield, therefore, electric field in the region III is zero.