# Over a certain region of space, the electric potential is v=5x− 3x^2y+ 2yz . . Find the expressions for the x, y, and z components of the electric field over this region. What is the magnitude of the field at the point P that has coordinates (1, 0, -2) m?

$\boldsymbol{E} = - \boldsymbol{\nabla} V$
= - ( (del_x(5x− 3x^2y+ 2yz)),(del_y (5x− 3x^2y+ 2yz) ),(del_z (5x− 3x^2y+ 2yz)))
:. bbE = ((E_x),(E_y),(E_z))= - ( ( 5 − 6x y ),( − 3x^2 + 2 z ),( 2y ) )
${\boldsymbol{E}}_{\text{(1, 0, -2)}} = \left(\begin{matrix}- 5 \\ 7 \\ 0\end{matrix}\right)$
$\implies \left\mid {\boldsymbol{E}}_{\text{(1, 0, -2)}} \right\mid = \sqrt{74}$