Question

Two infinitely long parallel conducting plates having surface charge densities $+\sigma$ and $-\sigma$ respectively, are separated by a small distance. The medium between the plates is vacuum. It ${\epsilon }_0$ is the dielectric permittivity of vacuum, then the electric field in the region between the plates is:

• A. $0V/m$
• B. $\sigma /2{\epsilon }_{0}V/m$
• C. $\sigma /{\epsilon }_{0}V/m$
• D. $2\sigma /{\epsilon }_{0}V/m$

Answer 1

Answer: (C)

Given that conducting plates have surface charge densities $+\sigma$ and $-\sigma$ respectively. Since the sheet is large, the electric field $F$ at energy point near the sheet will be perpendicular to the sheet.

The resultant electric field is given by
$E^{\prime }=E+E=2E$
If $\sigma$ is surface charge density then, electric field
$E^{\prime }=\frac{{\sigma }^{\prime }}{2{\epsilon }_0}$
$\therefore 2E=\frac{2\sigma }{2{\epsilon }_0}=\frac{\sigma }{{\epsilon }_0}V/m$