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Question

The work done by an external force to bring a third point charge q3=+e from infinity to x=2a is

A
e24πε0a
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B
e28πε0a
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C
e28πε0a
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D
e24πε0a
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Solution

The correct option is A e28πε0a
The work that must be done on q3 by an external force Fext is equal to the difference between two quantities: the potential energy U associated with q3 when it is at x = 2a and the potential energy when it is infinitely far away.

The second of these two is zero, so the work that must be done is equal to U. The distances between the charges are r13=2a and r22=a, so

W=U=q34πε0(q1r13+q2r23)
=+e4πε0(e2a+ea)=+e28πε0a

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