Question

Electric potential in space $V\left(x , y , z\right)=\left(x^{2} + y^{2} + z^{2}\right)V$ . If the magnitude of electric field strength E at $\left(1 m , 0 m , 2 m\right)$ in $NC^{- 1}$ is $4.47\times 10^{n}$ then find $n$ :

Answer 1

$E =-\left(\frac{\partial V }{\partial x }+\frac{\partial V }{\partial y } \hat{ j }+\frac{\partial V }{\partial z } \hat{ k }\right)$
$=-(2 x \hat{ i }+2 y \hat{ j }+2 z \hat{ k })$
$\overrightarrow{ E }=-(2 \hat{ i }+0 \hat{ j }+4 \hat{ k })$
$E =\sqrt{20}=2 \sqrt{5}=4.47 \quad N \quad C ^{-1}=4.47 \times 10^{0} \quad N \quad C ^{-1}$