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. $0V{m}^{-1}$
• B. $\frac{\sigma }{2{\epsilon }_0}V{m}^{-1}$
• C. $\frac{\sigma }{{\epsilon }_0}V{m}^{-1}$
• D. $\frac{2\sigma }{{\epsilon }_0}V{m}^{-1}$

Answer 1

Answer: (C)

$\frac{\sigma }{{\epsilon }_0}V{m}^{-1}$

We know that the field due to charge sheet is $E=\frac{\sigma }{2{ϵ}_0}$
Here the field in between the plates is $E=E_1+E_2=\frac{\sigma }{2{ϵ}_0}+\frac{\sigma }{2{ϵ}_0}=\frac{\sigma }{{ϵ}_0}V/m$