Bruce Harvey's Alternative Physics site

The Field Interaction Equations


vocacity, Kross, Kross product, electric field, magnetic field, Biot, Savart, law of Biot-Savart, Faraday, Faraday's law
There are two types of energy density field; electric energy density fields and magnetic energy density fields. The interaction of these two types of field is governed by the field interaction equations

In addition to the energy density vectors, these equations also contain two completely new concepts, and . The vector (Greek letter upsilon ) represents the fundamental property of motion proportional to the Kinetic Energy per unit of mass. I have named this vocasity. It is calculated from the velocity as

and the name comes from V Over C All Squared + ity.

The vector operation ; (shall we call it the Kross product ) is similar to the cross product, but has the term replaced by .

where is a unit vector perpendicular to the plane containing and and in the sense that a right hand thread would advance if rotated from to . Unfortunately the vector Kross product is only distributive across addition for parallel vectors.

Vocasity is more fundamental than velocity. A fact which can easily be verified experimentally by driving a friend's car into a tree at 10 mph and then your own car at 20 mph. The four fold increase in vocasity can be seen from the depth of the trunk prints.

Electric and magnetic fields are energy density fields. We should describe them by their energy densities. The Electric energy density and the Magnetic energy density are related to the familiar electric intensity and magnetic induction by the equations:


The Biot Savart law and Faraday's law can be derived from the field interaction equations by substituting these relationships and taking square roots.

It must be understood that neither the field interaction equations nor the laws of Faraday and Biot Savart are universally applicable. The field interaction equations are the second and third most fundamental of all physics equations. However, they apply to single fields. This means that the first should only be used in situations where one electric energy density field is dominant. This limitation does not apply to the second field interaction equation because there is only one magnetic energy density field present at any one point in space.

It will be noted that these equations not relativistic. They require a concept of absolute, or locally absolute velocity.

The behaviour of magnetic energy density flux (flux is the substance of a field) is too complex to be described by any one equation. We might almost say that it has a life of its own. The first field interaction equation should be treated as a statement of desirability. Provided nothing untoward is happening a moving electric energy density field will generate a magnetic energy density field according to the first field interaction equation. However, magnetic energy density flux must obey the following laws:

All this makes the exact behaviour of magnetic phenomena very difficult to capture in individual equations.

To get correct answers in all circumstances, we have to abandon the old concept of magnetic flux based on the magnetic induction ; and think in terms of magnetic energy density flux based on the magnetic energy density . This is because energy is the real nature of everything. If we want to calculate the force on a charge, we have to look at the amount of energy that is passing through its surface and calculate the velocity of that flux by dividing by the magnetic energy density at the surface. This is a tedious process, but as can be seen from the sections on inertia and the acceleration of a charge, it does give results consistent with the principle of conservation of energy.

Electrical engineers should not get worried at this point because the tendency has been to evolve machines which behave predictably. An example would be the attempts of the Victorians to measure current with a "current balance". When the mathematics of the Biot Savart law failed to give the right answers, a current balance was invented which worked on the mutual inductance of two coils.

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© Copyright Bruce Harvey 1997.