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  4. A and B are two thin concentric hollow conducting spheres of radii a and 2 a having charge 2 Q Q respectively if potential of outer sphere is 5 V then potential at inner sphere will be :

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Q. $A$ and $B$ are two thin concentric hollow conducting spheres of radii a and $2 a$ having charge $2 Q$ & $Q$ respectively if potential of outer sphere is $5\, V$ then potential at inner sphere will be :

Solution:

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$5=\frac{ kQ }{2 a }+\frac{ k 2 Q }{2 a }$
$=\frac{3}{2} \frac{ kQ }{ a }$
$\frac{ kQ }{ a }=\frac{10}{3}$
$V _{ in }=\frac{ k 2 Q }{ a }+\frac{ kQ }{2 a }$
$=\frac{5}{2} \frac{ kQ }{ a }=\frac{5}{2} \times \frac{10}{3}$
$=\frac{25}{3}$ volt