$A$ uniform electric field exists in the plane of the paper as shown. Here $A, B, C$, and $D$ are points on the circle. $V_{A}, V_{B}, V_{C}$, and $V_{D}$ are the potentials at those points respectively. Then:

$A$ uniform electric field of magnitude $E = 100 \ V/m$ is directed along the line $y = x + 3$. Find the potential difference $V_A - V_B$ between points $A(3, 1)$ and $B(1, 3)$.

The figure shows three points $A$,$B$,and $C$ in a region of uniform electric field $\overrightarrow{E}$. The line $AB$ is perpendicular and $BC$ is parallel to the field lines. Which of the following relations holds good? Let $V_A$,$V_B$,and $V_C$ represent the electric potential at points $A$,$B$,and $C$ respectively.

Describe schematically the equipotential surfaces corresponding to
$(a)$ a constant electric field in the $z$-direction,
$(b)$ a field that uniformly increases in magnitude but remains in a constant (say,$z$) direction,
$(c)$ a single positive charge at the origin,and
$(d)$ a uniform grid consisting of long equally spaced parallel charged wires in a plane.

The figure shows two parallel equipotential surfaces $A$ and $B$ kept a small distance $r$ apart from each other. $A$ point charge of $q$ coulomb is taken from the surface $A$ to $B$. The amount of net work done will be

Show that the direction of the electric field at a given point is normal to the equipotential surface passing through that point.