Question

An infinite conducting sheet has surface charge density $\sigma$. The distance between two equipotential surfaces is $r$. The potential difference between these two surfaces is

• A. $\frac{\sigma r}{2{\epsilon }_0}$
• B. $\frac{\sigma r}{{\epsilon }_0}$
• C. $\frac{\sigma }{{\epsilon }_{0}r}$
• D. $\frac{\sigma }{2{\epsilon }_{0}r}$

Answer 1

The correct option is B $\frac{\sigma r}{{\epsilon }_0}$


The electric field due to infinite conducting sheet is constant in magnitude along both sides of the sheet which is given by,

$E=\frac{\sigma }{{ϵ}_0}$

At each side $\overrightarrow{E}$ is uniform thus equipotential surfaces will be equally spaced.

Thus applying , $\Delta V=Ed$, we get potential difference for the space between two equipotential surfaces $(d=r)$ as,

$\Delta V=\frac{\sigma }{{\epsilon }_0}r$

Hence, option (a) is the correct answer.

why this question? caution: $\Delta V=Ed$ can be applied only for situation when charge moves along the direction of electric field.