Electric potential at any point $V =-\sqrt{23}x+4y+5z$, then magnitude of electric field is

8

The correct answer is Option (4) - 8

$\vec E=-∇V$

and,

$E_x=\frac{∂V}{∂x},E_y=\frac{∂V}{∂y},E_z=\frac{∂V}{∂z}$

Given,

$V=-\sqrt{123}x+4y+5z$

$E_x=-\frac{∂V}{∂x}=-(-\sqrt{23})=\sqrt{23}$

$E_y=-\frac{∂V}{∂y}=-(4)=-4$

$E_z=-\frac{∂V}{∂z}=-(5)=-5$

$|\vec E|=\sqrt{(\sqrt{23})^2+(-4)^2+(-5)^2}$

$=\sqrt{23+16+25}$

= 8 units