Electrical Engineering ⇒ Topic : Equipotential Surface

Equipotential Surface

Any surface over which the potential is constant is called an equipotential surface.In other words, the potential difference between any two points on an equipotential surface is zero. For example,consider two points A and B on an equipotential surface as shown in Fig. (a) .

                                                   FIGURE (A)/

                                    V_B - V_A   =   0                   V_B = V_A

The two important properties of equipotential surfaces are

(A) Work done in moving a charge over an equipotential surface is zero.

                                     Work done = Charge X P.D

Since potential difference (P.D.) over an equipotential surface is zero, work done is zero. 

(B)The electric field (or electric lines of force) are *perpendicular to an equipotential surface. 

Some cases of Equipotential surfaces. The fact that the electric field lines and equipotential surfaces are mutually perpendicular helps us to locate the equipotential surfaces when the electric field lines are known.

(1) Isolated point charge. The potential at a point P at a distance r from a point charge +q is given by ;

It is clear that potential at various points equidistant from the point charge is the same. Hence, in case of an isolated point charge, the spheres concentric with the charge will be the equipotential surfaces as shown in Fig. (b). Note that in drawing the equipotential surfaces, the potential difference is kept the same, i.e., 10 V in this case. It may be seen that distance between charge and equipotential surface I is small so that E (= dv/dr = 10/dr) is high. However, the distance between charge and equipotential surfaces II and III is large so that E (= dv/dr = 10/dr) is small. It follows,therefore, that equipotential surfaces near the charge are crowded (i.e., more E) and become widely spaced as we move away from the charge.

                                                       figure (b)

                                                figure (c)

(2) Uniform electric field. In case of uniform electric field (e.g., electric field between the plates of a charged parallel-plate capacitor), the field lines are straight and equally spaced. Therefore,equipotential surfaces will be parallel planes at right angles to the field lines as shown in Fig. (c).