Question

In x-y co-ordinate system if potential at a point P(x, y) is given by $V = axy$; where a is a constant, if r is the distance of point P from origin then electric field at P is proportional to

• A. r
• B. r^–1
• C. r^—2
• D. r²

Answer 1

Answer: (A)

r

Answer 2

By using $E = - \frac{dV}{dr}$ $E_{x} = - \frac{dV}{dx} = - ay$,

$E_{y} = - \frac{dV}{dy} = - ax$

Electric field at point P $E = \sqrt{E_{x}^{2} + E_{y}^{2}} = a\sqrt{x^{2} + y^{2}} = ar$ i.e., E ∝ r