The equation of an equipotential line in an electric field is $y = 2x$, then the electric field strength vector at $(1, 2)$ may be

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.

Draw an equipotential surface for dipole.

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?

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$[A]$ 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

A uniformly charged solid sphere of radius $R$ has potential $V_0$ (measured with respect to $\infty$) on its surface. For this sphere the equipotential surfaces with potentials $\frac{{3{V_0}}}{2},\;\frac{{5{V_0}}}{4},\;\frac{{3{V_0}}}{4}$ and $\frac{{{V_0}}}{4}$ have rasius $R_1,R_2,R_3$ and $R_4$ respectively. Then