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

Two point charges $-Q$ and $+Q / \sqrt{3}$ are placed in the $xy$-plane at the origin $(0,0)$ and a point $(2,0)$,respectively,as shown in the figure. This results in an equipotential circle of radius $R$ and potential $V = 0$ in the $xy$-plane with its center at $(b, 0)$. All lengths are measured in meters.
$(1)$ The value of $R$ is. . . . meter.
$(2)$ The value of $b$ is. . . . . .meter.

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:

On rotating a point charge having a charge $q$ around a charge $Q$ in a circle of radius $r$,the 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.

$A$ charge $+Q$ is placed at the centre of a circular path of radius $r$. The work done to bring a charge $+q$ from one end of the diameter to the other end of the circular path in the electric field produced by charge $+Q$ is $.......$