The electric potential $V$ at any point $(x, y, z)$, all in metres in space is given by $V=4 x^{2}$

Question

The electric potential $V$ at any point $(x, y, z)$, all in metres in space is given by $V=4 x^{2}$ volt. The electric field at the point $(1,0,2)$ in volt/meter, is

Professor PC Thomas Classes · Answer

$\vec{E}=-\left[\hat{i} \frac{\partial V}{\partial x}+\hat{j} \frac{\partial V}{\partial y}+\hat{k} \frac{\partial V}{\partial z}ight]$

Here, $V=4 x^{2} \quad 	herefore \quad \vec{E}=-8 x \hat{i}$
The electric field at point $(1,0,2)$ is
$$
\vec{E}_{(1,0,2)}=-8 \hat{i} \mathrm{Vm}^{-1}
$$

So electric field is along the negative $X$-axis.