The electric potential at a point $(x, y, z)$ is given by $V=-x^{2} y-x z^{3}+4$. The electric field

Question

The electric potential at a point $(x, y, z)$ is given by $V=-x^{2} y-x z^{3}+4$. The electric field at that point is

Professor PC Thomas Classes · Answer

The electric potential at a point,
$$
V=-x^{2} y-x z^{3}+4
$$

The field $\vec{E}=-\vec{
abla} V=-\left(\frac{\partial V}{\partial x} \hat{i}+\frac{\partial V}{\partial y} \hat{j}+\frac{\partial V}{\partial z} \hat{k}ight)$
$	herefore \quad \vec{E}=\hat{i}\left(2 x y+z^{3}ight)+\hat{j} x^{2}+\hat{k}\left(3 x z^{2}ight)$