Question

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

• A. $V=-xy+\text{constant}$
• B. $V=-(x+y)+\text{constant}$
• C. $V=-(x^2+y^2)+\text{constant}$
• D. $V=\text{constant}$

Answer 1

The correct option is A $V=-xy+\text{constant}$

$dV=-\overrightarrow{E}.\overrightarrow{dr}$
$=-(y\hat{i}+x\hat{j}).(dx\hat{i}+dy\hat{j}+dz\hat{k})$
$=-(ydx+xdy)=-d\left(xy\right)$
Integrating, we get
$V=-xy+\text{constant}$