Question

The plates of a parallel plate capacitor are charged with surface densities ${\sigma }_1$ and ${\sigma }_2({\sigma }_1=\sigma$ and ${\sigma }_2=-\sigma )$ respectively and placed horizontally. The electric field at points :

• A. inside the region between the plates will be zero
• B. above the upper plate and below the lower plate will be zero
• C. everywhere in space will be zero
• D. inside the region between the plates will be uniform and non zero (neglecting other effects)

Answer 1

Answer: (B), (D)

The correct options are
B above the upper plate and below the lower plate will be zero
D inside the region between the plates will be uniform and non zero (neglecting other effects)

The electric field due to charged plate, $E=\frac{\sigma }{2{ϵ}_0}$
The field lines are shown in figure.
The electric field above the upper plate, $E=\frac{\sigma }{2{ϵ}_0}+\frac{-\sigma }{2{ϵ}_0}=0$
Electric field at the center,$E=\frac{\sigma }{2{ϵ}_0}+\frac{\sigma }{2{ϵ}_0}=\frac{\sigma }{{ϵ}_0}$
Electric field below the lower plate,$E=\frac{\sigma }{2{ϵ}_0}+\frac{-\sigma }{2{ϵ}_0}=0$
Ans: $\left(B\right),\left(D\right)$