Q. Electric potential at any point is $V = - 5x + 3y + \sqrt{15z},$ then the magnitude of the electric field is
A) $3\sqrt{2}$
B) $4\sqrt{2}$
C) $5\sqrt{2}$
D) 7
Explanation
(d) $E_{x} = - \frac{dV}{dx} = - ( - 5) = 5;E_{y} = - \frac{dV}{dy} = - 3$
And $E_{z} = - \frac{dV}{dz} = - \sqrt{15}$
$E_{net} = \sqrt{E_{x}^{2} + E_{Y}^{2} + E_{Z}^{2}} = \sqrt{(5)^{2} + ( - 3)^{2} + \left( - \sqrt{15} \right)^{2}} = 7$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.