Electric potential at a point (x,y) in x - y plane is given by V = - kxy . field intensity at a dist

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2. Electric Potential and Capacitance

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

A

${r^2}$

B

$r$

C

$\frac{1}{r}$

D

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

Solution

(b) ${E_x} = – \frac{{dV}}{{dx}} = – \,ky$; ${E_y} = – \frac{{dV}}{{dy}} = \, – kx$
$E = \sqrt {E_x^2 + E_y^2} = k\sqrt {{x^2} + {y^2}} = kr$=

$E \propto r$

Standard 12

Physics

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