For given $\vec E = 2x\hat i + 3y\hat j$, find the potential at $(X, Y)$ if potential at origin is $5\, volts.$
Medium
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$\int_{5}^{\mathrm{V}} \mathrm{dV}=-\int_{(0,0)}^{(\mathrm{X} , \mathrm{Y})} \mathrm{E} \cdot \mathrm{dr}=-\int_{0}^{\mathrm{X}} \mathrm{E}_{\mathrm{X}} \cdot \mathrm{dx}-\int_{0}^{\mathrm{Y}} \mathrm{E}_{\mathrm{Y}} \mathrm{dy}$
$V-5=\frac{-2 X^{2}}{2} \frac{-3 Y^{2}}{2}$
$V=\frac{-2 X^{2}}{2} \frac{-3 Y^{2}}{2}+5$
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