Question

# Two infinite sheets having charge densities σ1 and σ2 are placed in two perpendicular planes whose two-dimensional view is shown in Fig. The charges are distributed uniformly on the sheet in electrostatic equilibrium condition. Four points are marked I, II, III, and IV. The electric field intensities at these points are →E1,→E2,→E3,and→E4, respectively. The correct expression for the electric field intensities is :

A
|E1|=|E2|=σ21+σ222ε0|E4|
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B
|E2|=|E4|=σ21+σ222ε0
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C
|E1|=|E2|=|E3|=|E4|=σ21+σ222ε0
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D
none of these
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Solution

## The correct option is C |→E1|=|→E2|=|→E3|=|→E4|=√σ21+σ222ε0Using the principle of superposition →E due to infinite plane sheet having surface charge density σ on its one face is σ/2ε0.So→E1=σ12ε0i+σ22ε0j→E2=−σ12ε0i+σ22ε0j→E3=−σ12ε0i−σ22ε0j→E4=σ12ε0i−σ22ε0j|→E1|=|→E2|=|→E3|=|→E4|=√σ21+σ222ε0

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