First slide

Electrostatic potential

Question

If electric potential at any point is V = -6x + 2y+ 9z, 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

11

Solution

$E_{x} = - \frac{dV}{dx} = - (- 6) = 6; E_{y} = - \frac{dV}{dy} = - 2 and E_{z} = - \frac{dV}{dz} = - 9 E_{net} = \sqrt{E_{x}^{2} + E_{y}^{2} + E_{z}^{2}} = \sqrt{36 + 4 + 81} = \sqrt{121} = 11$

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