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Question

Two infinite sheets having charge densities σ1 and σ2 are placed in two perpendicular planes whose two-dimensional view is shown in the figure. The charges are distributed uniformly on the sheets 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=E3=σ21+σ222ε0E4
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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+σ222ε0

Electric field due E due to infinite sheet of charge density σ is,E=σ2ε0The directions of electric field at all the poins due the perpendicular sheet are shown below.


Net electric field at point I:

EI=σ12ε0^i+σ22ε0^j

Net electric field at point II:

EII=σ22ε0^jσ12ε0^i

Net electric field at point III:

EIII=σ12ε0^iσ22ε0^j

Net electric field at point IV:

EIV=σ12ε0^iσ22ε0^j

So,
EI=EII=EIII=EIV=(σ12ε0)2+(σ22ε0)2

EI=EII=EIII=EIV=σ21+σ222ε0

Hence, option (c) is the correct answer.

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