Potential Gradient and Relation between Electric Field and Potential
An electric f...
Question
An electric field is given by →E=(y^i+x^j)N/C. The work done in moving a 1C charge from −→rA=(2^i+2^j)m to −→rB=(4^i+^j)m is
A
+4J
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B
−4J
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C
+8J
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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 WA→B=q(VB−VA)……(1) B∫AdV=−B∫A→E.d→r ⇒VB−VA=−(4,1)∫(2,2)(y^i+x^j).(dx^i+dy^j+dz^k) ⇒VB−VA=−(4,1)∫(2,2)(ydx+xdy) =−(4,1)∫(2,2)d(xy)=[−xy]4,12,2=0 ∴WA→B=0 [from Eq. (1)]