**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:

**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 V_{i}, which contains an amount of charge q_{i}. The distances between charges within the volume element V_{i}are much smaller as compared to r, the distance between V_{i}and P. In the limit where V_{i}becomes infinitesimally small, we may define a volume charge density as

Electric field due to a small charge element q_{i}at point P

The dimension of is charge/unit volume (C/m^{3}) 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

**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/m^{2}) in SI units. The total charge on the entire surface is

**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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