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Question

The electric potential at a point (x, y) in the x-y plane is given by V = - Kxy. The field intensity at a distance r in this plane, from the origin is proportional to :

A
r2
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B
r
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C
1/r
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D
1/r2
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Solution

The correct option is B r
Let the xy coordinates of the point at distance r from the origin be given as x=rcosθ, y=rsinθ
Potential is given as V=Kxy
Now, Electric field intensity is E=(dV/dx)i+(dV/dy)j=K(yi+xj)=K(rsinθi+rcosθj)=Kr(sinθi+cosθj)r
So electric field potential is proportional to r.

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