An infinite plane sheet of charge density \( 10^{-8}\,\mathrm{C\,m^{-2}} \) is held in air. In this situation, the distance between two equipotential surfaces, whose potential difference is 10 V, will be
Answer & explanation
Correct answer: option 1
The correct answer is Option (1) → 17.7 mm
The field of an infinite plane sheet of charge is uniform and equal to \( E = \sigma/(2\varepsilon_0) \). In a uniform field the potential difference between two equipotential surfaces (planes parallel to the sheet) a distance \( d \) apart is \( V = E\,d \).
\( \displaystyle E = \frac{\sigma}{2\varepsilon_0} = \frac{10^{-8}}{2 \times 8.85\times10^{-12}} = 565\,\mathrm{V\,m^{-1}} \)
\( \displaystyle d = \frac{V}{E} = \frac{10}{565} = 1.77\times10^{-2}\,\mathrm{m} = 17.7\,\mathrm{mm} \)