Question

Three concentric spherical conducting shells of radii R, 2R and 3R having charges Q1, Q2 and Q3 respectively on their outer surface respectively. If the potential of shell of radius 2R is zero then...


Ans is (D) but I wish to know how the answer came. (The working of the solution)
Thanks a lot.​

Answer 1

Given :

Magnitude of charge on spherical conducting shell of radius R = $Q_1$

Magnitude of charge on spherical conducting shell of radius 2R = $Q_2$

Magnitude of charge on spherical conducting shell of radius 3R = $Q_3$

These three spheres are concentric .

To Find :

If the potential of shell of radius 2R is zero then which of the given options is correct ?

Solution :

The total potential of the shell of radius 2R is equal to the sum of the potentials due to 1st , 2nd and 3rd sphere .

So we have :

$\frac{KQ_1}{2R} + \frac{KQ_2}{2R} + \frac{KQ_3}{3R} = 0$

Or, $\frac{Q_1}{2R}+ \frac{Q_2}{2R} + \frac{Q_3}{3R} = 0$

Or, $\frac{Q_1+ Q_2 }{2} + \frac{Q_3}{3} = 0$

Or, $3(Q_1 + Q_2) + 2Q_3 = 0$

Or, $3(Q_1 + Q_2) = -2Q_3$

Hence , correct option answer is option (d) i.e. $3(Q_1 + Q_2) = -2Q_3$ .