Q.

The electric potential at a point (x,y)  in the xy−  plane is given by                   V=−​K xy The electric filed intensity at a distance r  from the origin varies as

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a

r2

b

r

c

2 r

d

2 r2

answer is B.

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Detailed Solution

Co-ordinates of the point are (x,y) ∴       Distance of point from origin,r=x2+y2V=−K xyEx=−∂V∂x=−∂∂x(− Kxy)=KyEy=−∂V∂y=-∂∂y(− Kxy)=Kx∴    E=Ex2+Ey2=K y2+x2=Kr∴  E  α  r
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