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JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Electrostatics

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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 cylinder
(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
  1. (A)(A)✓ Correct
  2. (B)(B)
  3. (C)(C)
  4. (D)(D)

Answer: (A)

Solution

For a cylindrical charge distribution, the electric field at distance from the axis (where is greater than or equal to the radius of the charge distribution) is:



where is the linear charge density. The potential difference is:



When charge is given to the inner cylinder, an electric field exists in the region between the cylinders, creating a potential difference. When charge is given only to the outer cylinder, the field inside (between the cylinders) is zero by Gauss's law, so no potential difference appears. Statement (A) is correct.

JEE Advanced · 2007 · 08 Apr 2007 · Paper 1 · Single correct option

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