Three equal charges are placed at the corners of an equilateral triangle. Which of the graphs below correctly depicts the equally-spaced equipotential surfaces in the plane of the triangle? (All graphs have the same scale.)

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

Figure shows a set of equipotential surfaces. The magnitude and direction of electric field that exists in the region is .........

An infinite non-conducting sheet has a surface charge density $\sigma  = 0.10\, \mu C/m^2$ on one side. How far apart are equipotential surfaces whose potentials differ by $50\, V$

Two point charges of magnitude $+q$ and $-q$ are placed at $\left( { - \frac{d}{2},0,0} \right)$ and $\left( {\frac{d}{2},0,0} \right)$, respectively. Find the equation of the equipotential surface where the potential is zero.

A point charge $+Q$ is placed just outside an imaginary hemispherical surface of radius $R$ as shown in the figure. Which of the following statements is/are correct?

(IMAGE)

$[A]$ The electric flux passing through the curved surface of the hemisphere is $-\frac{\mathrm{Q}}{2 \varepsilon_0}\left(1-\frac{1}{\sqrt{2}}\right)$

$[B]$ Total flux through the curved and the flat surfaces is $\frac{Q}{\varepsilon_0}$

$[C]$ The component of the electric field normal to the flat surface is constant over the surface

$[D]$ The circumference of the flat surface is an equipotential