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

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

BITSATBITSAT 2018

Solution:

$E_{x}=-\frac{r v}{r x}=\frac{-r}{r x}(-5 x+5 y+\sqrt{15 z})=5$
$E_{y}=\frac{r v}{r y}=-3 E_{z}=-\sqrt{15}$
Now, $E=\sqrt{E_{y}^{x}}+E_{y}^{z}+E_{z}^{z}=7$