4.1 INTRODUCTION

We have dealt with an electric field due to different charge configurations using Coulomb s law. Then we dealt with similar problems of finding electric field intensity, but not without symmetrical distribution of flux density, using Gauss s law. As soon as symmetry in the problem is missing, it turns complicated because the conditions required for the Gaussian surface leaves the complicated integration behind. For example, if we think of applying Gauss s law for finding the density of flux due to a point charge off-centered from the origin, the representation of a Gaussian surface in equations becomes a little complicated, and solving the double integral over a closed surface is even more complicated. On the other hand, if one needs to find a resultant electric field due to point charge, infinite line charge, and infinite charged sheet, which can be conveniently expressed using unit vectors in spherical, cylindrical, and Cartesian coordinates respectively, then one has to use a common coordinate system for its vector addition. In short, a task of conversion of spherical and cylindrical vector fields into Cartesian coordinates needs to be exercised. Now, if we plan to use a scalar field to represent the vector electric field ( E), then scalar addition becomes comparatively simple. The question of symmetry will also be automatically smoothened, as it will be a scalar representation of the vector quantity of the electric field E. To smoothly reach this scalar term known as Potential ( V), we shall first...