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
$E .4 \pi r^{2}=\frac{Q_{\text {en }}}{\epsilon_{0}}=\frac{Q_{A}}{\epsilon_{0}}$
or $E=\frac{Q_{A}}{4 \pi \epsilon_{0} r^{2}}$
for $r_{A}< r< r_{B}$
By Gauss's law, the field $E$
for $r>r_{B}$ is $E .4 \pi r^{2}=\frac{Q_{e n}}{\epsilon_{0}}=\frac{Q_{A}-Q_{B}}{\epsilon_{0}}$
$E=\frac{Q_{A}-Q_{B}}{4 \pi \epsilon_{0} r^{2}}$ for $r>r_{B}$
As $\left| Q _{ B }\right|>\left| Q _{ A }\right|, E$ is negative for $r > r _{ B }$.