WHAT ARE THE PROPERTIES OF EQUIPOTENTIAL SURFACES ?????????
Equipotential surfaces strictly speaking are orthogonal trajectories of electric field lines(mathematically:- orthogonal trajectories are a family of curves in the plane that intersect a given family of curves at right angles ).Whats it really means is that any electro static(conservative) field line penetrates such a surface normally(i.e. it is locally perpendicular at the point of penetration). The value of electrostatic potential at any two or more given points on such a surface is the same and is a constant. The work done by the field force in moving a charge along this surface is zero because there is no difference in potential between the initial and final points.Another way of understanding this fact is that since the net electric field vector is perpendicular to the surface and has no component along the surface(i.e. tangential component) so no force acts on a charged particle along the surface and hence no work is done even if the particle is already moving along the surface. Mathematically the gradiant of the surfaces represents the negative of the direction of the net electric field vector consistent with the equation E = -¶V/¶r ( bold face represents a vector).