Question

Define an equipotential surface. Draw equipotential surfaces : 

(i) in the case of a single point charge and

(ii) in a constant electric field in Z-direction. why the equipotential surfaces about a single charge are not equidistant ?

(iii) Can electric field exist tangential to an equipotential surface ? Give reason.

Answer 1

Equipotential surface is a surface which has equal potential at every Point on it.

(i) Equipotential surfaces due to single point charge are concentric sphere having charge at the centre.

(ii) In constant electric field along z-direction, the perpendicular distance between equipotential surfaces remains same.

For single charge, equipotential surface will be series of concentric spherical shells  with charge at centre,

the separation dr between equipotential surface will go on increasing with decrease in electric field.

(iii) No, because if the surface is not equipotential then it would mean that there is tangential component of electric field along surface. This component will result in motion of electrons, but since we have static fields, this is not possible.

Answer 2

(i) An equipotential surface is that at every point of which electric potential is the same. Due to a single point charge, equipotnetial surfaces are centred at the charge, As \(V \propto \frac{1}{r}\), the equipotential surfaces
about a single charge cannot be equidistant.

(ii) In a constant electric field in Z- direction, equipotential surfaces lie in XY plane perpendicular to Z-direction as shown in Fig.

(iii) As electric field is perpendicular to the equipotential surface, the field cannot exist tangenital to the equipotential surface.