First slide

Electrostatic potential

Question

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

Difficult

A

r²
B

r
C

1/r
D

1/r²

Solution

Given that V = -k x y
$E_{x} = - \frac{\partial V}{\partial x} = ky$
and $E_{y} = - \frac{\partial V}{\partial y} = kx$
$\begin{aligned} ∴ E_{r} = \sqrt{(E_{x}^{2} + E_{y}^{2})} = \sqrt{(k^{2} y^{2} + k^{2} x^{2})} \\ = k \sqrt{(x^{2} + y^{2})} = k \cdot r \end{aligned}$
So, $E_{r} \propto r$ .

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