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  4. The electric field on two sides of a large charged plate is shown in the diagram. 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) <img class=img-fluid question-image alt=Question src=https://cdn.tardigrade.in/q/nta/p-wye53e8qoljw.png />

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Q. The electric field on two sides of a large charged plate is shown in the diagram. The charge density on the plate in S.I. units is given by ( $\epsilon _{0}$ is the permittivity of free space in S.I. units)

Question

NTA AbhyasNTA Abhyas 2020Moving Charges and Magnetism

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.

Solution

$∴ \, \, \, \text{E}_{0} + \text{E} = 1 2 V m^{- 1}$
$\text{E}_{0} - \text{E} = 8 V m^{- 1}$
Solving equations, E = 2 V m-1 and E0 = 10 V m-1
Now, electric field due to plate $= \frac{\sigma }{2 \epsilon _{0}} = 2$
$∴ \, \sigma = 4 \epsilon _{0}$