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 following figure shows the electric potential $V$ as a function of position $x$ across $4$ regions on the $x$-axis. Which of the following is correct for the electric field $E$ in these regions?

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:

Assume that an electric field $E = 30x^2 \hat{i}$ exists in space. If $V_0$ is the potential at the origin and $V_A$ is the potential at $x = 2 \ m$,then the potential difference $(V_A - V_0)$ is: (in $V$)

Two large plane parallel conducting plates are kept $10 \ cm$ apart as shown in the figure. The potential difference between them is $V$. The potential difference between the points $A$ and $B$ (shown in the figure) is

In a certain region of space,the variation of potential with distance from the origin as we move along the $x$-axis is given by $V = 8x^2 + 2$,where $x$ is the $x$-coordinate of a point in space. The magnitude of the electric field at a point $(-4, 0)$ is .......... $V/m$.