What is the equipotential surface? Draw the equipotential surface due to point charge.

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Equipotential SurfaceThe surface in an electric field where the value of electric potential is the same at all the points on the surface is called equipotential surface. The potential difference between two points in an equipotential surface is zero. Thus, work done in moving the charge from one point to another in an equipotential surface is zero. since the work is done is zero when the direction of force (electric field) and displacement is normal. Thus, electric field is perpendicular to the plane in an equipotential surface. It is to be noted for the equipotential surface:
1. For a uniform electric field $$ \vec{E} $$, the equipotential surface is normal to its field lines. According to figure 3.8,1
(a) II and III are equipotential surfaces.
2. For an isolated point charge:Potential at a distance r due to point charge $$ +\mathrm{q} $$
$$V=\dfrac{1}{4 \pi \varepsilon_{0}} \dfrac{q}{r}$$
If we draw a sphere of radius r surrounding the $$ + $$ q charge. Then, potential will be same at all points on the sphere i.e., equipotential surfaces are spherical whose charge is at the centre. For a positive point charge, as the radius of the spherical surface increases, the potential of spherical surface decreases.
3. Equipotential surface for an electric dipole: The equipotential surface for an electric dipole are shown dotted in figure 3.8 ( $$ \mathrm{c} $$ ).
4. Equipotential surfaces for a pair of similar point charges: The equipotential surface is as shown in figure$$ 3.8(\mathrm{d}) $$

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