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 volt/m
• B. $\sigma /2{\epsilon }_0$ volt/m
• C. $\sigma /{\epsilon }_0$ volt/m
• D. $2\sigma /{\epsilon }_0$ volt/m

Answer 1

The correct option is C $\sigma /{\epsilon }_0$ volt/m

The electric field at any point in between plates due to $+\sigma$ is $E_{+}=\frac{\sigma }{2{ϵ}_0}$

The electric field at any point in between plates due to $-\sigma$ is $E_{-}=\frac{\sigma }{2{ϵ}_0}$

Both fields are acting in same direction (from + plate to - plate) so net field in between plates is $E=E_{+}+E_{-}=\frac{\sigma }{{ϵ}_0}$ volt/m