JEE Advanced 2007 Physics question

A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral.

(A)A potential difference appears between the two cylinders when a charge density is given to the inner cylinderCorrect
(B)A potential difference appears between the two cylinders when a charge density is given to the outer cylinder
(C)No potential difference appears between the two cylinders when a uniform line charge is kept along the axis of the cylinders
(D)No potential difference appears between the two cylinders when same charge density is given to both the cylinders

Answer: (A)

Solution

The potential difference between the cylinders depends only on the electric field in the space between them, which by Gauss's law is produced only by the charge enclosed within that region (the inner cylinder and anything inside it). (A) Charge on the inner cylinder creates a radial field

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Question ID VK-037407