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

The Correct Option is 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 $r > r _{ B }$.