A positive charge q is inside a hollow conducting sphere that has a uniform char

Question

A positive charge q is inside a hollow conducting sphere that has a uniform charge density of and radius RR; the charge is initially very close (Rdr) to the inner surface.

(a) Calculate and then enter the change in potential energy of the charge if it moves from point A to point B along the diameter.

(b) Calculate and then enter the change in potential energy of the charge if it moves from point A to point B along (just inside (Rdr) the curved inner surface.

A positive charge q is inside a hollow conducting sphere that has a uniform charge density of o and radius R; the charge is initially very close (R-dr to the inner surface. (a) Calculate and then enter the change in potential energy of the charge if it moves from point A to point B along the diameter. AU (b) Calculate and then enter the change in potential energy of the charge if it moves from point A to point B along just inside (R-dr the curved inner surface. AU

Explanation / Answer

First of all. Note that the potential energy due to electrostatic force is state dependent but not path dependent. So, no matter what the answer of both the parts is same since the initial and final state of the particle are same in both cases.

Now, according to the gauss's law, if there is no net charge enclosed by a closed surface then the electric field inside the surface has to be zero. Therefore, electric field inside the sphere is zero.

Now since electric field is zero and electric field is the derivative of electric potential, so the potential inside the surface will be constant. Therefore no potential difference occurs when moving along the diameter or along the inner surface.

Hence, no change in potential energy of charge q.

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