Prove that a closed equipotential surface with no charge within itself must enclose an equipotential volume.

This question has Statement $-1$ and Statement $-2$ Of the four choices given after the Statements, choose the one that best describes the two Statements

Statement $1$ : No work is required to be done to move a test charge between any two points on an equipotential surface

Statement $2$ : Electric lines of force at the equipotential surfaces are mutually perpendicular to each other

Two charges $2 \;\mu\, C$ and $-2\; \mu \,C$ are placed at points $A$ and $B\;\; 6 \;cm$ 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 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

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.)