First slide

Electrostatic potential

Question

If potential (in volts) in a region is expressed as V(x, y, z) = 6xy - y+ 2yz, the electric field (in N/C) at point ( 1, 1, 0) is :

Moderate

A

$- (6 \hat{i} + 6 \hat{j} + \hat{k})$
B

$- (3 \hat{i} + 5 \hat{j} + 3 \hat{k})$
C

$- (6 \hat{i} + 5 \hat{j} + 2 \hat{k})$
D

$- (2 \hat{i} + 3 \hat{j} + \hat{k})$

Solution

$\vec{E} = - \frac{\partial V}{\partial x} \hat{i} - \frac{\partial V}{\partial y} \hat{j} - \frac{\partial V}{\partial z} \hat{k} \vec{E} = - (6 y) \hat{i} - (6 x - 1 + 2 z) \hat{j} - (2 y) \hat{k}$
at point (1, 1, 0)
$\vec{E} = - 6 \hat{i} - 5 \hat{j} - 2 \hat{k} = - (6 \hat{i} + 5 \hat{j} + 2 \hat{k})$

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