First slide

Electric flux

Question

The electric field on two sides of a large charged plate is shown in figure. The charge density on the plate in SI units is given by ( $ε_{0}$ is the permittivity of free space in SI units)

Moderate

A

$2 ε_{0}$
B

$4 ε_{0}$
C

$10 ε_{0}$
D

$Zero$

Solution

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 E₀ is the external electric field. Therefore,
$\begin{array}{l} ∴ E_{0} + E = 12 {Vm}^{- 1_{}} . . . . . . . (i) \\ E_{0} - E = 8 {Vm}^{- 1} . . . . . . . . . (i i) \end{array}$
Solving Eqs. (i) and (ii), E = 2vm^-1and E₀= 10 Vm^-1
Now, electric field due to plate is $σ / 2 ε_{0} = 2$ . Therefore, $σ = 4 ε_{0}$

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