Electric potential at any point $V =-\sqrt{23}x+4y+5z$, then magnitude of electric field is
Answer & explanation
Correct answer: option 4
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