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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 potential difference appears between the two cylinders when a charge density is given to the inner cylinder.
A potential difference appears between the two cylinders when a charge density is given to the outer cylinder.
No potential difference appears between the two cylinders when a uniform line charge is kept along the axis of the cylinders.
No potential difference appears between the two cylinders when same charge density is given to both the cylinders.
Solution
$\mathrm{dV}=-\overrightarrow{\mathrm{E}} \cdot \mathrm{d} \overrightarrow{\mathrm{r}}$
and $\mathrm{E}=\frac{\lambda}{2 \pi \varepsilon_0 \mathrm{r}}$
where $\mathrm{r}$ is distance from the axis of cylindrical charge distribution ( $\mathrm{r}$ is equal to or greater than radius of cylindrical charge distribution).
