Thursday, 4 April 2013

Charge Distribution and Charge Density

Charge Distribution and Charge Density
The electric field due to a small number of charged particles can readily be computed using the superposition principle. But what happens if we have a very large number of charges distributed in some region in space? There may be these three kind of charge distributions:
  1. Volume Charge Distribution and Volume Charge Density
    Suppose we wish to find the electric field at some point P. Let's consider a small volume element Vi, which contains an amount of charge qi. The distances between charges within the volume element Vi are much smaller as compared to r, the distance between Vi and P. In the limit where Vi becomes infinitesimally small, we may define a volume charge density  as

    Electric field due to a small charge element qi at point P

    The dimension of  is charge/unit volume (C/m3) in SI units. The total amount of charge within the entire volume V is

    The concept of charge density here if analogous to mass density  m. When a large number of atoms are tightly packed within a volume, we can also take the continuum limit and the mass of an object if given by

  2. Surface Charge Distribution and Surface Charge Density
    In a similar manner, the charge can be distributed over a surface S of area A with a surface charge density  (lowercase Greek letter sigma). Here surface charge density can be written as

    The unit of   is (C/m2) in SI units. The total charge on the entire surface is

  3. Linear Charge Distribution and Linear Charge Density
    If the charge is distributed over a line of length l, then the linear charge density  (lowercase Greek letter lambda) is

    where the unit of  is (C/m). The total charge is now an integral over the entire length

Note: If charge are uniformly distributed throughout the region, the densities () then become uniform and can be written as:

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