Calculation of Charge Density

Calculation of Charge Density The charge on the charged body can be considered as continuously distributed.

The charge density can measure the density of this charge distribution. The charge of the volume distribution is measured by the volume density of the charge, that of the area distribution by the charge surface density, and the line distribution by the charge linear density. When the charge is distributed inside an object, the amount of electricity per unit volume is called the body charge density. In nature, there are two kinds of charges, positive and negative. The charge density may also depend on location.

Figure 1.

Charge Density

Free charge and bound charge

Bound charges set up electric dipoles in response to an applied electric field E, and polarize other nearby dipoles tending to line them up. The net accumulation of charge from the orientation of the dipoles is the bound charge. They are called bound because they cannot be removed: in the dielectric material the charges are the electrons bound to the nuclei.

Free charges are the excess charges which can move into electrostatic equilibrium, i.e. when the charges are not moving and the resultant electric field is independent of time, or constitute electric currents.

Overall solutions

In quantum mechanics, charge density ρq is related to wavefunction ψ(r) by the equation ρq(r)=q|ψ(r)|

2

2

where q is the charge of the particle and |ψ(r)| = ψ*(r)ψ(r) is the probability density function i.e. probability per unit volume of a particle located at r.

When the wavefunction is normalized - the average charge in the region r ∈ R is 3

where d r is the integration measure over 3d position space.