First slide

Electrostatic potential

Question

The potential field of an electric field $\vec{E} = (y \hat{i} + x \hat{j})$ is

Moderate

A

V = -xy + constant
B

V = -(x + y) + constant
C

V = -(x2 +/)+constant
D

V = constant

Solution

$dV = - \vec{E} \cdot d \vec{r} = - (y \hat{i} + x \hat{j}) \cdot (dx \hat{i} + dy \hat{j}) = - (y d x + x d y) = - d (x y)$
Integrating, we get V = -.xy+constant

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