Question

Electric potential in volt (in region) is given by
$V=6x+8y+4z^{2}$
Calculate the electric force (in $N$ ) acting on $2C$ point charge placed at origin.

Answer 1

$E_{x}=-\frac{\partial V}{\partial x}=-6\hat{i}$
$E_{y}=-\frac{\partial v}{\partial y}=-8\hat{j}$
$E_{z}=-\frac{\partial V}{\partial z}=-8z\hat{k}$
$\overset{ \rightarrow }{E}_{net}$ at origin $=\sqrt{6^{2} + 8^{2}}=10$
$\Rightarrow \left|\overset{ \rightarrow }{F}\right|=\left|q \overset{ \rightarrow }{E}\right|=20N$