The electric potential in a region of space is given by $V=\left(5x-7x^{2}y+8y^2+16yz-4z\right) volts$ . The y-component of the electric field at the point (2, 4, -3) is

Given:

$V=\left(5x-7x^{2}y+8y^2+16yz-4z\right) volts$

Point: (2,4,-3)

To find: y - component of electric field

Solution:

$\overrightarrow{E}=-\left(\frac{\partial V}{\partial x}\hat{i}+\frac{\partial V}{\partial x}\hat{j}+\frac{\partial V}{\partial x}\hat{k}\right)$

$\Rightarrow E_y=-{\overline{)\frac{\partial V}{\partial y}}}_{(x,y,z)}$

$\Rightarrow E_y=-{\overline{)\frac{\partial }{\partial y}\left(5x-7x^{2}y+8y^2+16yz-4z\right)}}_{(2,4,-3)}$

$\Rightarrow E_y={\overline{)\left(7x^2-16y-16z\right)}}_{\left(2,4,-3\right)}$

$\Rightarrow E_y=12 V/m$