1.14 Continuous Charge Distribution

       We have so far dealt with charge configurations involving discrete charges q1,12,....,1n. One reason why we restricted to discrete charges is that the mathematical treatment is simpler and does not involve calculus. For many purposes, however, it is impractical to work in terms of discrete charges and we need to work with continuous charge distributions.
       
         Consider a case that grains are spread uniformly over the floor, just one layer so that the floor is not at all seen. Now, what is the total number of grains? It is a laborious task to count one by one. So what can we do? Let us consider a unit area and count the number of grains in that area. Multiply this number by the total area and we can get the total number of grains. The number of grains per unit area can be called as surface grain density.
        
           Similarly, when charges are distributed over a finite space, it is useful to consider the density of charge. It is used in three different ways.

            i. Linear Charge Density
 (1) It is the charge per unit length. If Q charges distributed uniformly over a length 'l' then

                                lamda = Q/l

            ii. Surface Charge Density:
          It is the charge per unit area. If 'Q' charge is distributed uniformly in area 'A', then surface charge density sigma = Q/A

             iii. Volume Charge Density
           It is the charge per unit volume. If 'Q'  charge is distributed uniformly in a volume V, then volume charge density row = Q/V