Question

# Two parallel plane sheets 1 and 2 carry uniform charge densities σ1 and σ2 (see Fig. 20.8). The electric field in the region marked I is (σ1>σ2). (Consider the right direction as the positive direction)

A

σ12ϵ0

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B

σ22ϵ0

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C

(σ1+σ2)2ϵ0

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D

(σ1σ2)2ϵ0

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Solution

## The correct option is C −(σ1+σ2)2ϵ0 The left sheet 1 produces a field of magnitude E1=σ12ϵ0 which points away from it, to the left in region I and to the right in regions II and III. The right sheet 2 produces a field of magnitude E2=σ22ϵ0 which points away from it, to the left in regions II and I and to the right in region III. If σ1>σ2>0 the field in each region from the principle of superposition will be as follows: Region I : E=12ϵ0(σ1+σ2) towards left. Region II: E=12ϵ0(σ1−σ2) towards right. Region III: E=12ϵ0(σ1+σ2) towards right.

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