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

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

Answer 1

Answer: (C)

$\sigma / \varepsilon_{0} V / m$

Answer 2

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 $E'=E+E=2 E$ If $\sigma$ is surface charge density then, electric field $E'=\frac{\sigma'}{2 \varepsilon_{0}}$ $\therefore 2 E =\frac{2 \sigma}{2 \varepsilon_{0}}=\frac{\sigma}{\varepsilon_{0}} V / m$