The electric potential at a point $(x, y, z)$ is given by $V=-x^2y-xz^3 +4 $. The electric field at that point is
AIPMT 2009, Easy
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The electric potential at a point,
$V=-x^{2} y-x z^{3}+4.$
The field $\vec{E}=-\vec{\nabla} V=-\left(\frac{\partial V}{\partial x} \hat{i}+\frac{\partial V}{\partial y} \hat{j}+\frac{\partial V}{\partial z} \hat{k}\right)$
$\therefore \vec{E}=\hat{i}\left(2 x y+z^{3}\right)+\hat{j} x^{2}+\hat{k}\left(3 x z^{2}\right)$
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