Q. The electric potential at any point $x,\ y,\ z$ in meters is given by$V = 3x^{2}$. The electric field at a point (2,0,1) is
A) $12\ Vm^{- 1}$
B) $- 6\ Vm^{- 1}$
C) $6\ Vm^{- 1}$
D) $- 12\ Vm^{- 1}$
Explanation
(d) Here, electric potential
$V = 3x^{2}$
Electric field,
$E = - \frac{\partial V}{\partial x}$
$= - \frac{\partial}{\partial x}\left( 3x^{2} \right) = - 6x\ $
$\therefore E_{(2,\ 0,1)} = - 12Vm^{- 1}$
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.