A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral. [2007]

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. [2007]

Smart Achievers · Accepted Answer

(1)

According to Gauss's theorem, the electric field between two cylinders is $E = \frac{λ}{2 π ε_{0} r} .$ This electric field will produce a potential difference $d V = - \vec{E} \cdot d \vec{r} .$ When a charge density is given to the inner cylinder, the potential developed at its surface is different from that on the outer cylinder. This is because the potential decreases with distance for a charged conducting cylinder when the point of consideration is outside the cylinder.

But when a charge density is given to the outer cylinder, it will change its potential by the same amount as that of the inner cylinder. Hence, no potential difference will be produced between the cylinders.

Solution

Q.
A long, hollow conducting cylinder is kept coaxially inside another long, hollow conducting cylinder of larger radius. Both the cylinders are initially electrically neutral. [2007]

1 A potential difference appears between the two cylinders when a charge density is given to the inner cylinder.

2 A potential difference appears between the two cylinders when a charge density is given to the outer cylinder.

3 No potential difference appears between the two cylinders when a uniform line charge is kept along the axis of the cylinders.

4 No potential difference appears between the two cylinders when same charge density is given to both the cylinders.

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