A solid conducting sphere, having a charge Q , is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the out

Question

A solid conducting sphere, having a charge Q , is surrounded by an uncharged conducting hollow spherical shell. Let the potential difference between the surface of the solid sphere and that of the outer surface of the hollow shell be V . If the shell is now given a charge of – 4 Q , the new potential difference between the same two surfaces is:

TestHub · Accepted Answer

First condition:

Both conducting spheres are shown.
$V_{i n} - V_{o u t} = (\frac{K Q}{r_{1}}) - (\frac{K Q}{r_{2}})$
$\Rightarrow V = K Q (\frac{1}{r_{1}} - \frac{1}{r_{2}})$
Second condition:

Shell is now given charge $- 4 Q$ .
$V_{i n} - V_{o u t} = (\frac{K Q}{r_{1}} - \frac{4 K Q}{r_{2}}) - (\frac{K Q}{r_{2}} - \frac{4 K Q}{r_{2}})$
$= \frac{K Q}{r_{1}} - \frac{K Q}{r_{2}}$
$= K Q (\frac{1}{r_{1}} - \frac{1}{r_{2}}) = V$

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