First slide

Electrostatic potential

Question

Find the potential V of an electrostatic field $\vec{E} = a (y \hat{i} + x \hat{j})$ , where a is a constant.

Moderate

A

$axy + C$
B

$- axy + C$
C

$axy$
D

$- axy$

Solution

$\vec{E} = a (y \hat{i} + x \hat{j})$
$V_{2} - V_{1} = - \int (ay dx + ax dy)$
Take $V_{1} = C and V_{2} = V .$ Then
$V = - a \int (ydx + xdy) + C$
$= - a \int d (yx) + C = - axy + C$

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