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Q.

Let V0  be the potential at the origin in an electric field E→=Exi^+Eyj^. The potential at the point (x,y)  is

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a

V0−xEx−yEy

b

V0+xEx+yEy

c

xEx+yEy−V0

d

(x2+y2)Ex2+Ey2−V0

answer is A.

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Detailed Solution

Ex=−∂V∂x Ey=−∂V∂yIf y is constant (=0),∫V0VAdV=−∫0xExdxOr VA−V0=−Exx.Where x is constant (=x),∫VAVBdV=−∫0yEydyOr VB−VA=−Eydy .Adding, VB−V0=−xEx−yEyOr VB=V0−xEx−yEy .
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Let V0  be the potential at the origin in an electric field E→=Exi^+Eyj^. The potential at the point (x,y)  is