The electric potential V at any point (x, y, z) in space is given by V = 6x2 volt, where all the distances are measured in metre. The electric field at the point (1 m, 0, 2 m) is
Answer & explanation
Correct answer: option 2
The potential V is a scalar function, whereas the field $\vec{E}$ is a vector function. The three components of $\vec{E}$ are given as
$E_{x}=-\frac{\partial V}{\partial x}=-\frac{\partial}{\partial x}\left(6 x^2\right)=-12 x$
$E_{y}=-\frac{\partial V}{\partial y}=-\frac{\partial}{\partial y}\left(6 x^2\right)=0$
$E_z=-\frac{\partial V}{\partial z}=-\frac{\partial}{\partial z}\left(6 x^2\right)=0$
at the given point, x = 1,
∴ $\vec{E} = -12\hat{i}$
Hence, answer (b) is correct.