Question

The electric field on two sides of a large charged plate is shown. The charge density on the plate in S.I units is given by (${ϵ}_0$ is the permittivity of free space in S.I units)

• A. Zero
• B. $2{ϵ}_0$
• C. $4{ϵ}_0$
• D. $10{ϵ}_0$

Answer 1

The correct option is C

$4{ϵ}_0$

From the figure, it is clear that the plate is placed in an external electric field. Let the electric field due
to plate be E, and $E_0$ is the external electric field.

$\therefore E_0+E=12V{m}^{-1}$

$E_0-E=8V{m}^{-1}$

Solving equations, $E=2V{m}^{-1}$ and $E_0=10V{m}^{-1}$

Now, electric field due to plate =$\frac{\sigma }{2{ϵ}_0}=2\therefore \sigma =4{ϵ}_0$