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

-12$\hat{i}$ V/m

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.