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Question

A point charge q moves from point P to a point S along a path PQRS in a uniform electric field E pointing parallel to the x-axis. The coordinates of P, Q. R and S are (a,b,0),(2a,0,0),(a,b,0) and (0,0,0). The work done by the field in the above process is :

A
zero
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B
qEB
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C
qEa
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D
qEa
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Solution

The correct option is C qEa
As the field E is uniform, so E is constant at every point.
As E is directed parallel to x axis, so E=E^i
The work done , W=F.dr=qE^i.(^idx+^jdy+^kdz)
W=qEdx=qE[2aadx+a2adx+0adx]=qE[2aa+a2a+0a]=qEa

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