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Question

Two charges Q & Q are kept at some distance, so that electric field at the mid point is E. Find the force on Q due to the field of Q. (charges are isolated)

A
QE4
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B
4QE
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C
QE8
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D
QE2
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Solution

The correct option is C QE8

Let E+ be electric field at mid point due to positive charge,
E be electric field at mid point due to negative charge

Let distance between the charges be r.

The electric field at the midpoint,
E=E++E
=kQ(r/2)2^i+kQ(r/2)2^i=8kQr2^i
[taking positive x axis in rightward direction]

At position Q, the field due to Q is EQ=kQr2^i=E8

Therefore, the force on charge Q is F=QE8

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