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

Show that the direction of electric field at a given is normal to the equipotential surface passing through that point.

A uniform electric field pointing in positive $x$-direction exists in a region. Let $A$ be the origin, $B$ be the point on the $x$-axis at $x = + 1$ $cm$ and $C$ be the point on the $y$-axis at $y = + 1\,cm$. Then the potentials at the points $A$, $B$ and $C$ satisfy

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

Draw an equipotential surface for dipole.