This is one section from the Mathematics of the Pure Charge Theory. It is located on this separate page to speed downloading times.

mass, inertia, electric charge, charge, kinetic energy, field of motion (1), (2)

The acceleration produces a change in the magnetic field given by

and we can expand these to get three more equations.

The effect of acceleration on a body is twofold. The speed of the body may change and its direction of motion may change. There are two special cases: acceleration parallel to the velocity changes only the speed; acceleration perpendicular to the velocity changes only the direction. When we consider a single spherical charge, the effects on the field of motion are a change in its energy content caused by a change in speed and a rotation caused by a change in direction. The movement of magnetic energy density flux is constrained so that it can only move parallel to the electric field of the charge. Furthermore, the electric field is fixed in direction and cannot rotate. So rotation of the magnetic field is accomplished by the movement of energy density flux both into and out of the charge.

A simplistic approach might be to differentiate the first equation for with respect to time to give

This does not however take into account the fact that magnetic energy density flux has vector like properties. If in a small time the magnetic intensity changes from to , the energy density vector changes from to . However, the vector addition of must have the same geometry as that of . If we draw vector triangles to represent the addition, they must be similar.

We look to the vector triangle from which the limiting result for is derived and scale it by a factor of .

This means that

At this point, it is best to enter into Cartesian coordinates and simplify the vector product because algebraic expansion would introduce extra sines and cosines of unknown angles. We have

The magnitude is easy enough to work out as giving

Which gives

At this point, we are in danger of running into complications. We really need this vector in the form of a magnitude times a unit vector, but this expression is rather messy. So we will delay dealing with this problem by making a substitution.

Then we can write

This is a rate of change of the magnetic energy density vector. We need to divide the space surrounding the charge in such a way as to facilitate integration. We do this by dividing it into conic elements extending outwards from the sphere with rectangular cross section by . In a conic element, the rate of change of the magnetic energy density is inversely proportional to fourth power of the radius

To find the velocity with which magnetic energy density flux is flowing from the surface of the charge, we must divide by the energy density times the area of the surface of the charge within the conic element. Note that at this point, we need the magnitude and so we omit the direction which is given by the unit vector .

What we need to understand here is that we are generating (or adsorbing) magnetic energy density flux at the surface of the charge. Its energy density is the same as the energy density that is already there, but its directional property is different. The value of to use is given by

Now we find that and are reunited and we can substitute for .

The force felt by the charge acting on the surface within the conic element is

where the factor ½ is the penetration coefficient. This is needed because the surface of the charge has a finite thickness. Energy density flux is generated throughout the thickness of the surface. We have used the value of at the outer face of the surface, but this is its maximum value and we need to average it over the thickness of the surface.

We find that effecting the change in the field of motion generates a force proportional to and opposing the acceleration. Thus a simple spherical charge with no other properties has an inherent electromagnetic reaction to acceleration. The charge has the property which we call

where is now the force required to accelerate the charge and

The inertial mass of a pure charge is thus dependent on its charge and its radius.

When we consider real electrons and take the charge on an electron together with the Bohr radius of the electron and Einstein's *E = mc ^{2}*, we can calculate that the mass equivalent of the energy of the electric field of an electron is

The similarity in the two suggests that we are close to explaining the inertial of electrons as a purely electromagnetic phenomena.

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© Copyright Bruce Harvey 1997.