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 \varepsilon_{0} r} $
$\Delta V =-\frac{\lambda}{2 \pi \varepsilon_{0}} \int\limits_{a}^{b} \frac{d r}{r}=\frac{\lambda}{2 \pi \varepsilon_{0}} \ln \left(\frac{a}{b}\right)$

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