Question

If electric potential at any point is $V=-5 x+3 y+\sqrt{15} z$, where $V, x, y$ and $z$ are in SI units, then the magnitude of the electric field (in SI unit) is

• A. $3 \sqrt{2}$
• B. $4 \sqrt{2}$
• C. $5 \sqrt{2}$
• D. 7

Answer 1

Answer: (D)

$E_{x}=-\frac{d V}{d x}=-(-5)=5 ;$
$E_{y}=-\frac{d V}{d y}=-3$
and $E_{z}=-\frac{d V}{d z}=-\sqrt{15}$
$E_{\text {net }}=\sqrt{E_{x}^{2}+E_{y}^{2}+E_{z}^{2}}$
$=\sqrt{(5)^{2}+(-3)^{2}+(-\sqrt{15})^{2}}=7$