First slide

Electrostatic potential

Question

If electric potential at any point is V = -5x + 3 y + $\sqrt{15}$ z, where V, x, y and z are in SI units, then the magnitude of the electric field (in SI unit) is

Moderate

A

$3 \sqrt{2}$
B

$4 \sqrt{2}$
C

$5 \sqrt{2}$
D

7

Solution

$E_{x} = - \frac{dV}{dx} = - (- 5) = 5; E_{y} = - \frac{dV}{dy} = - 3 and E_{z} = - \frac{dV}{dz} = - \sqrt{15} E_{net} = \sqrt{E_{x}^{2} + E_{y}^{2} + E_{z}^{2}} = \sqrt{(5)^{2} + (- 3)^{2} + (- \sqrt{15})^{2}} = 7$

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