Question

Electric potential at any point is $V=-5x+3y+\sqrt{15}z$, then the magnitude of electric field is __________ $N/C$

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

Answer 1

The correct option is C $7$

$V=-5x+3y+\sqrt{15}z$

$\overrightarrow{E}=-\frac{\partial V}{\partial x}\hat{i}-\frac{\partial V}{\partial y}\hat{j}-\frac{\partial V}{\partial z}\hat{k}$

Now $\frac{\partial V}{\partial x}=-5$

$\frac{\partial V}{\partial y}=3$

$\frac{\partial V}{\partial z}=\sqrt{15}$

$\overrightarrow{E}=5\hat{i}-3\hat{j}-\sqrt{15}\hat{k}$

$⟹E=\sqrt{5^2+(-3{)}^2+(\sqrt{15}{)}^2}$

$⟹E=\sqrt{25+9+15}$

$⟹E=7N/C$

Answer-(C)