$A$ 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 $B(1, 3)$.

Given below are two statements: one is labelled as Assertion $(A)$ and the other is labelled as Reason $(R)$.
Assertion $(A)$: Work done by an electric field on moving a positive charge on an equipotential surface is always zero.
Reason $(R)$: Electric lines of force are always perpendicular to equipotential surfaces.
In the light of the above statements,choose the most appropriate answer from the options given below:

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.

Two charges $2 \; \mu C$ and $-2 \; \mu C$ are placed at points $A$ and $B$ which are $6 \; cm$ apart.
$(a)$ Identify an equipotential surface of the system.
$(b)$ What is the direction of the electric field at every point on this surface?

$A$ uniform electric field is prevailing in the $X$-direction in a certain region. The coordinates of points $P$,$Q$,and $R$ are $(0,0)$,$(2,0)$,and $(0,2)$ respectively. Which of the following alternatives is true for the potentials at these points?

$A$ square of side $a$ has a charge $Q$ at its centre. $A$ charge $q$ is placed at one of the corners. The work required to be done in moving the charge $q$ from this corner to the diagonally opposite corner is