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

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

A
$3 \sqrt{2}$
B
$4 \sqrt{2}$
C
$5 \sqrt{2}$
D
7

Solution:

$\vec{E} = \hat{i} \frac{d v}{d x} + \hat{j} \frac{d v}{d y} + \vec{k} \frac{d v}{d z}$

$E_{x} = - \frac{dV}{dx} = - (- 5) = 5, E_{y} = - \frac{dV}{dy} = - 3$ and $E_{z} = - \frac{dV}{dz} = - \sqrt{15}$

$∴ E_{net} = \sqrt{E_{x}^{2} + E_{y}^{2} + E_{z}^{2}} = \sqrt{(5)^{2} + (- 3)^{2} + (- \sqrt{15})^{2}} = 7$

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