Two thin concentric conducting spherical shells of radii R and 3R carry charges +Q and -2Q respectively. A point charge +q is moved slowly from a point on the surface of the inner shell to a point on the surface of the outer shell along a spiral path. The work done by the external agent in this process is :

Step-by-step solution

The work done by an external agent in moving a charge q slowly between two points is W_ ext = q(V_ final - V_ initial ) . Because the electrostatic field is conservative, the spiral path is irrelevant. The potential at any point is the superposition of the potentials due to both shells. Potential at the surface of the inner shell (radius R ): V_ in = V_ inner shell + V_ outer shell V_ in = 1 4 ₀ Q R + 1 4 ₀ -2Q 3R = 1 4 ₀ ( 3Q - 2Q 3R ) = Q 12 ₀ R Potential at the surface of the outer shell (radius 3R ): V_ out = V