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

Three infinitely long wires with linear charge density $\lambda$ are placed along the $x$-axis,$y$-axis,and $z$-axis respectively. Which of the following denotes an equipotential surface?

The figure shows three points $A, B$ and $C$ in a region of uniform electric field $E$. The line $A B$ is perpendicular and $B C$ is parallel to the field lines. Then,which of the following holds good? ($V_{A}, V_{B}$ and $V_{C}$ represent the electric potential at points $A, B$ and $C$,respectively)

The figure shows two equipotential lines in the $XY$ plane for an electric field. The scale is shown. The $X$-component $E_x$ and $Y$-component $E_y$ of the electric field in the space between the equipotential lines are respectively:

If charge $+q$ is taken from one point to another over an equipotential surface, then

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.