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Question

A large charged conducting sheet is placed in a uniform electric field, perpendicularly 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 V/m and on the right it is E2=3×105 V/m. The sheet experiences a net electric force of 0.08 N. Find the area of one face of the sheet.( Assume the external field to remain constant after introducing the large sheet)

[k=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
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Solution

The correct option is A 3.6π×102 m2
Let the external field be E0 and surface charge density of sheet be σ (including both surfaces)



Electric field due to induced charge σ is given by E=σ2ε0
So, from the diagram we can deduce that

E1=E0E and E2=E0+E

Solving these two equations we get,

E0=E1E22 and E=E1E22

From the data given in the question,

E0=(53)×1052=105 V/m

E=(53)×1052=4×105 V/m

and , σ2ε0=4×105

σ=8ε0×105 V/m

Force on sheet, F=qEo
F=σAE0

Substituting the given data we get,

0.08=8ε0×105×A×105

A=10128.85×1012 or 3.6π×102 m2

Hence, option (a) is the correct answer.

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