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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 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 :
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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=qE∫dx=qE[∫2aadx+∫a2adx+∫0adx]=qE[2a−a+a−2a+0−a]=−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=qE∫dx=qE[∫2aadx+∫a2adx+∫0adx]=qE[2a−a+a−2a+0−a]=−qEa
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