A conducting sphere has a net charge of +Q . Points A and B are on opposite sides of the surface of the sphere. If a point charge +q is moved from point A to point B in a straight line through the center of the sphere, the work done to move the charge is WC . If a point charge +q is moved from point A to point B along the surface of the sphere, the work done is WS . How do Wc and Ws compare?
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WC is greater than WS. This is because when the charge is moved along the surface of the sphere, it experiences a repulsive force from the net charge of +Q, which requires additional work to move the charge.
Wc= Ws because while as the electric field inside a conductor is zero, there is no force that acts on the charge as it passes through the conductor resulting in zero work using the common definition of work as Fd = W. On the other hand there is a force that exists on the outside of the sphere as that is where the charges of the conducting sphere are located however those are parallel to the area vector (perpendicular to the surface) and thus when the charge moves along the sphere's surface it is effectively moving along an equipotential line and perpendicular to the electric force, thus it experiences no work either.
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