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Question

# V0 is the potential at the origin in an electric field. →E=Ex→i−Ey→j. The potential at the point (x,y) is:V0−xEx+yEyV0+xEx+yEy√x2+y2√E2x+E2y−V0xEx+yEy−V0

A
x2+y2E2x+E2yV0
B
V0xEx+yEy
C
V0+xEx+yEy
D
xEx+yEyV0
Solution
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#### We knowV(x1)−V(x2)=∫x2x1Edx.Now potential change in x directionVx(x)−Vx(o)=∫oxExdx=−Exx.Vx(x)=Vx(o)−ExxPotential change in y directionVy(y)−Vy(o)=∫oy(−Ey)dy=+EyyVy(y)=Vy(o)+EyyNow total potential at (x,y)=Vx+Vy=Vx(o)−Exx+Vy(o)+Eyy=Vo−xEx+yEy

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