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Charge Behaviour

Consider two ...

Question

Consider two concentric spherical metal shells of radii 'a' and b> a. The outer shell has charge Q , but the inner shell has no charge,Now,the inner shell is grounded. This means that the inner shell will come at zero potential and that electric fields lines leave the outer hell and end on the inner shell.

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Solution

$V_{A} = \frac{K (q_{1} + q_{2})}{R}$
Potential at sphere $B$
neglecting sphere $e$ , $A$
$V_{B} = \frac{{K q}_{2}}{r}$
Net potential at $B$ ,
$V_{C} = V_{A} - V_{B}$
$V_{C} = \frac{K (q_{1} + q_{2})}{R} - \frac{K q_{2}}{r}$
Final potential at the surface of $B$
$V_{f} = V_{A} + V_{C}$
$V_{f} = \frac{K (q_{1} + q_{2})}{R} + \frac{K (q_{1} + q_{2})}{R} - \frac{K q_{2}}{r}$
$V_{f} = K (\frac{2 (q_{1} + q_{2})}{R} - \frac{q_{2}}{r})$

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