The figure represents two equipotential lines in the $x-y$ plane for an electric field. The $x$-component $E_{x}$ of the electric field in the space between these equipotential lines is, (in $V/m$)

The variation of potential $V$ with distance $x$ from a fixed point is as shown in the figure. The electric field at $x = 13\,m$ is......$V/m$.

The potential difference between two points $A(2, 1, 0) \ m$ and $B(0, 2, 4) \ m$ in an electric field $\vec{E} = (x \hat{i} - 2y \hat{j} + z \hat{k}) \ Vm^{-1}$ is: (in $V$)

The electric potential in some region is expressed by $V = 6x - 8xy^2 - 8y + 6yz - 4z^2 \text{ volt}$. The magnitude of the electric force acting on a charge of $2 \text{ C}$ situated at the origin will be $-$ (in $\text{ N}$)

If the electric potential at a point $P(x, y)$ is given by $V = axy$,then the electric field at a distance $r$ from the origin is proportional to:

The electric field $\vec E$ between two points is constant in both magnitude and direction. Consider a path of length $d$ at an angle $\theta = 60^o$ with respect to the field lines as shown in the figure. The potential difference between points $1$ and $2$ is