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Question
Two parallel uniformly charged infinite plane sheets, '1' and '2', have charge densities + `sigma and -2sigma `respectively. Give the magnitude and direction of the net electric field at a point.
(i) in between the two sheets and
(ii) outside near the sheet '1'.
Solution
Which is same in both the case so it is independent of the size and shape of the closed surface
Let `hat6` be the unit vector directed from left to right
Let P and Q are two points in the inner and outer region of two plates respectively charge densities on plates are + `sigma and -2sigma`
(i) Electric field at point P in the inner region of the plates
`vec"E"_1 = sigma/(2epsilon_0) hat"r" and vec"E"_2 = (2sigma)/(2epsilon_0)hat"r"`
∴ Net electric field in the inner region of the plates (i.e., at P) is
`vec"E" = vec"E"_1 vec"E"_2`
`vec"E" = (sigma/(2epsilon_0)+ sigma/epsilon_0)hat"r"`
`vec"E" = (3sigma)/(2epsilon_0)hat"r"`
(ii) Electric field at point Q in the outer region of plate 1
`vec"E"_1 = sigma/(2epsilon_0)(-hat"r") and vec"E"_2 = (2sigma)/(2epsilon_0)hat"r"`
∴ Net electric field in the outer region of plate 1 (i.e. at Q ) is
`vec"E" = vec"E"_1 + vec"E"_2 = (sigma/epsilon_0 - sigma/(2epsilon_0))hat"r"`
`vec"E" = sigma/(2epsilon_0)hat"r"`
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