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Coulomb's Law

Coulomb's law is the fundamental law of the electric force between two stationary, charged particles. It has a form very similar to the universal law of gravitation. This law ststes that:

        |q1| |q2|         k is a constant,
F = k ---------        q1 and q2 are the charges on the particles,
             r^2             r is the distance between the particles.

Where does this law come from ?
Coulomb's law was experimentally established in 1785. It comes from direct observation and careful experimentataion. It can br derived by using Maxwell's equations for Electrostatics in free space as postulates. If you would like to see this derivation, please consult your textbook.

In this form, this law allows us to see why charged particles can attract and repel one another. The charge on the particles creates a force between them.

In electromagnetics, this form of Coulomb,s law is not very widely used. Rather than calculating a single force, it is useful to talk about a field of force. Thus we introduce the concept of the electric field intensity E. We define this quantity as follows:

                    F                   q1 _                     1        
    E = l i m  ---- V/m = k ----- r,
k = ----------------
       q2->0   q2                  r^2           
4 ¡¿pi ¡¿epsilon

This allows us to deal with the field of force surrounding charged particles as a vector field. Fortunately, the principle of superposition applies to the charged particles in an E field, allowing us to calculate the E field of both discrete and continuous distributions of charge. For discrete systems, the total field is just the vector sum of all fields caused by the individual charges. for continuous distributions, we can integrate to get the contribution of each element of the distribution.

One problem arises when we try to calculate the E field using Coulomb's Law : the mathematics starts to get very involved once the geometries start to get complex. This definition is always valid, but you may not want to handle the math. To take advantage of cases where symmetry can ease the math, the concept of Gauss's law is introduced.

You may be wondering why we would ever want to use Coulomb's law, if the math gets to difficult. There are several good reasons:

¢Ñ It is always valid, even in asymetrical cases.
¢Ñ It results in fairly simple expressions for E due to a small distribution of point charges. Far away from any geometrical system, the E field acts as if the system was a point charge. So if your only concern is how things react a reaonable distance away from the distribution, Coulomb's law can give you an accurate description.

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