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Question

A large charged metal sheet is placed in a uniform electric field, perpendicular to the electric field lines. After placing the sheet into the field, the electric field on the left side of the sheet is E1=5×105 Vm1 and on the right it is E2=3×105 Vm1. The sheet experience a net electric force of 0.08 N. Find the area of one face of the sheet. Assume the external electric field to remain constant after introducing the large sheet. Use (14πε0)=9×109 Nm2C2

A
3.6π×102 m2
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B
0.9π×102 m2
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C
1.8π×102 m2
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D
none of these
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Solution

The correct option is A 3.6π×102 m2
Let external electric field be E0 and surface charge density of sheet be σ(Including both surfaces). So,
EP=σ2ε0

Electric field due to sheet
E1=E0EP (i)E2=E0+EP (ii)

From (i) and (ii),
E0=E1E22=105 Vm1and EP=E1E22=4×105 Vm1σ2ε0=4×105 or σ=8ε0×105Force on sheetF=qE0 or 0.08=σAE0or 0.08=8ε0×105A×105A=1012ε0=1012×36×109π=3.6π×102 m2

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