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The electric potential at a point x , y in the x - y plane is given by V = - K x y The electric field intensity at a distance r from the origin varies as

Options

  1. Ar 2
  2. Br
  3. C2 r
  4. D2 r 2

Correct answer

B. r

Step-by-step solution

Co-ordinates of the point are (x, y) Distance of point from origin, r = x 2 + y 2 ,   V = - k x y E x = - ∂ V ∂ x = - ∂ ∂ x - k x y = k y E y = - ∂ V ∂ y = - ∂ ∂ y - k x y = k x   E = E x 2 + E y 2 = k y 2 + x 2 = k r

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