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SHM Formulae

The electric ...

Question

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

A

r^{2}

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B

r

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C

\frac{1}{r}

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D

\frac{1}{r^{2}}

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Solution

The correct option is B r
$E_{x} = - \frac{d V}{d x} = - k y; E_{y} = - \frac{d V}{d y} = - k x$

$E = \sqrt{E_{x}^{2} + E_{y}^{2}} = k \sqrt{x^{2} + y^{2}} = k r \Rightarrow E \infty r$

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