Electric potential at any point is V = -5x + 3y + √ {15} z , then magnitude of electric field

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2. Electric Potential and Capacitance

easy

Electric potential at any point is $V = -5x + 3y + \sqrt {15} z$, then the magnitude of the electric field is

A

$3\sqrt 2 $

B

$4\sqrt 2 $

C

$5\sqrt 2 $

D

$7$

Solution

$\mathrm{V}=-5 \mathrm{x}+3 \mathrm{y}+\sqrt{15} \mathrm{z}$

$\mathrm{E}_{\mathrm{x}}=-\frac{\mathrm{dV}}{\mathrm{dx}}=5 \quad ; \quad \mathrm{E}_{y}=-3: \mathrm{E}_{z}=-\sqrt{15}$

$\Rightarrow \mathrm{E}=\sqrt{25+9+15}$

$\Rightarrow \mathrm{E}=7$

Standard 12

Physics

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