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Question

An electric field is given by E=(y^i+x^j) N/C. The work done in moving a 1 C charge from rA=(2^i+2^j) m to rB=(4^i+^j) m is

A
+4 J
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B
4 J
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C
+8 J
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D
Zero
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Solution

The correct option is D Zero
A=(2,2) and B=(4,1)
Now WAB=q(VBVA) (1)
BAdV=BAE.dr
VBVA=(4,1)(2,2)(y^i+x^j).(dx^i+dy^j+dz^k)
VBVA=(4,1)(2,2)(ydx+xdy)
=(4,1)(2,2)d(xy)=[xy]4,12,2=0
WAB=0 [from Eq. (1)]

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