Question

Two concentric spherical shells have charges + q and - q as shown in figure. Choose the correct options :

• A. At A electric field is zero, but electric potential is non-zero
• B. At B electric field and electric potential both are non-zero
• C. At C electric field is zero but electric potential is non-zero
• D. At C electric field and electric potential both are zero

Answer 1

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

The correct options are
A At A electric field is zero, but electric potential is non-zero
B At B electric field and electric potential both are non-zero
D At C electric field and electric potential both are zero

Electric field inside a shell is zero. So at A field will be zero.

Potential at A is $V_A=kq/r_i-kq/r_o$ where $r_i=$ radius inner shell and $r_o=$ radius of outer shell.

as $r_i\ne r_o,V_A\ne 0$

At B: using Gauss's law the electric filed $E_B.4\pi r^2=\frac{q_{en}}{{ϵ}_0}=\frac{+q}{{ϵ}_0}\Rightarrow E_B=\frac{q}{4\pi {ϵ}_0{r}^2}\ne 0$

$V_B=kq/r+k(-q)/r_o\ne 0$

At C: using Gauss's law the electric filed $E_C.4\pi r^2=\frac{q_{en}}{{ϵ}_0}=\frac{+q-q}{{ϵ}_0}=0\Rightarrow E_C=0$

$V_C=kq/r_{ac}+k(-q)/r_{ac}=0$