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Three large parallel plates have unifrom...

Three large parallel plates have unifrom surface charge densities as shown in the figure. What is the electric field at `P`
.

A

` - ( 4 sigma)/( in_0) hat k`

B

` - ( 4 sigma)/( in_0) hat k`

C

` - ( 4 sigma)/( in_0) hat k`

D

` - ( 4 sigma)/( in_0) hat k`

Text Solution

Verified by Experts

The correct Answer is:
A, B, C, D
The elerctric field at a point `P` due to an infinite long plane sheet carrying a uniform charge density `sigma` is given by
`E = ( sigma)/( 2 varepsilon_0)`
It is independent of the distance of point `P` from the sheet and field is uniform. The direction of the electric field is away from the sheet and perpendicular for `sigma` is positive and is towards the sheet and peroendicular to it for (sigam) is negative. hence .
`vec E_1 = (sigma)/(2 varepsilon_0) (- hat k)`
From the superposition principle, the net elerctric field at point `P` is
`E = vec E_1 + vec E_2 + vec E_3`
`= (sigma)/(2 varepsilon_0) ( - hat k) + (2 sigma)/(2 varepsilon_0) (- hat K) + (3 sigma)/( 2 varepsilon_0) (- hat K) = (3 sigma)/(varepsilon_0) hat K`.
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