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 ${\epsilon }_0$ is the dielectric permittivity of vacuum, then the electric field in the region between the plates is

• A. 0 volts $/$ metre
• B. $\frac{\sigma }{2{\epsilon }_o}$ volts/metre
• C. $\frac{\sigma }{{\epsilon }_o}$ volts $/metre$
• D. $\frac{2\sigma }{{\epsilon }_o}$ 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
$=\frac{\sigma }{2{\epsilon }_0}+\frac{\sigma }{2{\epsilon }_0}$
$=\frac{\sigma }{{\epsilon }_0}$ volt/metre