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 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.

Answer 1

Answer: (A)

Let $\lambda$ be the charge density on the inner cylinder.
For $a<r<b$, we get
$E=\frac{\lambda }{2\pi {\epsilon }_{0}r}$
$\Delta V=-\frac{\lambda }{2\pi {\epsilon }_0}\underset{a}{\overset{b}{\int }}\frac{dr}{r}=\frac{\lambda }{2\pi {\epsilon }_0}\ln \left(\frac{a}{b}\right)$

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