Question

Two concentric conducting thin spherical shells $A$ and $B$ having radii $r_A$ and $r_B\left(r_B>r_A\right)$ are charged to $Q_A$ and $-Q_B\left(\left|Q_B\right|>\left|Q_A\right|\right)$. The electrical field along a line passing through the centre is

• A.
• B.
• C.
• D.

Answer 1

Answer: (A)

Here, $E=0$ for $0<r<r_A$ (as field inside shell is zero)
By Gauss's law, the field $E$ for $r_A<r<r_B$ is
$E.4\pi r^2=\frac{Q_{\text{en }}}{{ϵ}_0}=\frac{Q_A}{{ϵ}_0}$
or $E=\frac{Q_A}{4\pi {ϵ}_0{r}^2}$
for $r_A<r<r_B$
By Gauss's law, the field $E$
for $r>r_B$ is $E.4\pi r^2=\frac{Q_{en}}{{ϵ}_0}=\frac{Q_A-Q_B}{{ϵ}_0}$
$E=\frac{Q_A-Q_B}{4\pi {ϵ}_0{r}^2}$ for $r>r_B$
As $\left|Q_B\right|>\left|Q_A\right|,E$ is negative for $r>r_B$.