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. If $\varepsilon_{0}$ is the dielectric permittivity of vacuum, then the electric field in the region between the plates is

• A. 0 volts $/$ metre
• B. $\frac{\sigma}{2 \varepsilon_{o}}$ volts/metre
• C. $\frac{\sigma}{\varepsilon_{o}}$ volts $/ metre$
• D. $\frac{2 \sigma}{\varepsilon_{o}}$ volts/metre

Answer 1

Answer: (C)

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

If $\sigma$ is surface charge density then, electric field between the plates
$=\frac{\sigma}{2 \varepsilon_{0}}+\frac{\sigma}{2 \varepsilon_{0}}$
$=\frac{\sigma}{\varepsilon_{0}}$ volt/metre