Question

A long, hollow conducting cylinder is kept coaxially inside another 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 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 cylinders.

Hint:

In conductors, a potential difference exists only if there is an electric field between them.

Answer 1

The Correct Option is A

Step 1: When charge is given to the inner cylinder, equal and opposite charge is induced on the inner surface of the outer cylinder. Step 2: This produces an electric field in the region between the two cylinders.

Step 3: The presence of an electric field implies a potential difference between the two cylinders. 

Step 4:  • If charge is given only to the outer cylinder, the inner region remains field-free.
• A line charge on the axis produces equal potential on both cylinders.
• Same charge density on both cylinders results in no field between them. 

Hence, only option (A) is correct.