Electron structure           Home/EM

Overview

What makes an electron tick? Since electric and magnetic fields are so important to the behaviour of the electron, can they explain all its behaviour?

It is worth remembering that the electric and magnetic fields of the electron become extremely strong close to the electron with energy densities of over 10³⁰ Joules/m³, equivalent to a mass densities of over 10¹³ kg/m³, similar to that of compressed matter in a neutron star. These fields are many orders stronger than steel, more so because they lack the dislocations that affect the capabilities of steel.

Can an atom be stable?

There is a theory that states that the field model of an atom cannot be stable since a charged particle (the  electron in this case) radiates when it accelerates. Unlike photon energy, this radiated energy is broadband. An electron in a circular orbit undergoes centripetal acceleration, and hence the circular orbit of an electron in an atom will decay. The basis for this theory is that a charged particle radiates electromagnetic energy in an accelerating frame, increasing the work done to accelerate it - that is, its inertia is increased. If you are interested in the details you can search out “Radiation Reaction” on the web - although don’t be surprised if you come up with something quite unrelated!

However, it is not necessary to know the maths to find the flaw in the theory. There is no “absolute” viewpoint in space - what is acceleration from one viewpoint is deceleration from another, so whatever happens during acceleration must also happen during deceleration. So if an electron radiates as it accelerates, hence increasing its inertia, it must also radiate as it decelerates, similarly increasing its inertia.

First consider the acceleration...

E_in = E_k + E_r

The input energy E_in to accelerate an electron from our rest frame to a new rest frame is equal to the final kinetic energy = E_k plus the energy radiated during acceleration = E_r. No problem so far.

But now brake the electron from its new rest frame back into our own in exactly the same way. The electron in its accelerating/decelerating frame sees no difference between rest frames and radiates E_r as before. This radiation increases its inertia, so that we get...

E_k + E_r = E_out

So as expected, E_in = E_out (after all the acceleration and deceleration are identical from the electron’s point of view). But on the way two bursts of radiation have been lost to the system = 2.E_r. So we have recovered all the original input energy, PLUS energy has been radiated - so energy conservation is violated.

Now the above evaluation is not specific to any particlular theory - we have not used maths equations, but rather considered the general principles behind it. Hence every theory that claims an accelerating charge emits radiation will inherently violate the Law of the Conservation of Energy.

If we claim that Radiation Reaction applies to an electron in an atom, it seems to lead not so much to a decaying electron orbit, but rather to a stable orbit that continuously radiates from violation of conservation. If we claim that the Law of the Conservation of Energy applies, it leads to a orbit that does not radiate. The latter approach is taken here.

Of course there are issues to deal with - if Radiation Reaction is rejected on the grounds of violation of Conservation, how do we explain those phenomena currently attributed to it?

1. In the 19^th century it was thought that EM radiation from aerials was driven by the acceleration of electrons up and down the wire; Maxwell proved that it was the variable flow of electrons generating a variable magnetic field in the centre of a dipole, and the fluctuating electric field strengths caused by electron bunching at the ends of dipole - that is, changes in field strength lead to EM radiation from aerials, not the acceleration of charged particles.
2. “Braking Radiation” or Bremsstrahlung can be explained by the interaction of an electron with fields in the atoms of the target. In fact actual examples such as X-ray generators are far too efficient at low energies for this theory to be viable. Other related effects can be explained by the interaction of electrons with external fields.
3. The energy loss associated with the decaying spiral of charged particles in a magnetised cloud chamber may simply be the energy lost to the ionisation process that makes the track visible in the first place.

You can research these phenomena on the web and make up your own mind.

So from this section I take forward the concept that...

The Conservation of Energy requires that...

• accelerating or orbiting electrons do not dissipate energy by radiation.

Lorentz forces

If the electron is moving in the magnetic field it will “see” an electric field. This is induced by the relative motion of the magnetic field creating an electric field from E = ( v x B ), where v is the relative vector velocity of the magnetic field with respect to the electron, and B is the vector magnetic field strength, and E is the perceived vector electric field.

The induced electric field is always normal to the velocity vector, so the electron sees a transverse field that forces it sideways; this force is termed the “Lorentz Force”. Because it is normal to the velocity vector at all times it will turn the straight-line path of the electron into a curved one.

The following image shows the path of an electron entering a magnetic field from the right. The magnetic field has North pointing up out of the page and the electron has a velocity V...

Electric field rotation in a magnetic field

The very same field structure that causes electrons to flow when a superconducting coil is placed in a magnetic field also causes the electron to rotate in a magnetic field. So when a charged particle enters a magnetic field it will rotate at a speed that depends on the magnetic field strength.

Imagine an electron rotating on an axis that lies vertically up this page...

The electric field is shown directed towards the centre of the electron (because of its negative charge); the full distribution is of course spherical - it does not affect the argument to show only the horizontal plane of electric field lines. The moving radial electric flux lines induce a vertical magnetic field (from Maxwell’s third equation), with the magnetic North pointing down for the shown rotation.

Now consider the electron as a set of radial electric field lines. What happens when an electron is just entering a magnetic field? In the following image the field lines on the left of the electron enter the field first...

The electric field lines to the left enter the magnetic field first, and so experience the transverse Lorentz forces first. This presents an unequal force distribution that both accelerates the electron sideways, and starts it rotation in the direction shown.

The direction of rotation can be seen to generate a magnetic field with North down into the page - that is, opposing the external magnetic field. This cancels out the magnetic field in the proximity of the electron, but at the cost of increasing the magnetic field stress further away. Hence the total magnetic energy in the system is increased. The extra energy comes from the force that pushed the electron into the magnetic field, so it experiences a repulsive force that causes it to slow down on entering the field, giving up kinetic energy for magnetic energy. This behaviour exactly mirrors the situation where a superconducting coil is pushed into a magnetic field.

Note: this picture is very different from the older quantum mechanics view which defined all the electric field energy as residing at a single point, producing a magnetic dipole by orbiting around some notional centre of the electron; in this paper the radial electric field lines simply sweep round as the electron rotates, inducing a magnetic field according to Maxwell’s third equation - nothing is in any form of orbit, and the electric field energy is distributed throughout the field.

The stronger the magnetic field, the faster the rotation. Going from a lower magnetic field to a higher one will increase the rate of rotation, while going from a higher to a lower one will reduce it. If an electron is somehow brought to zero rotation inside a magnetic field, and moved to a different field strength, it is the difference in magnetic field that determines its new rate of rotation. If the new field strength is higher then the system (of electron plus external magnetic field) has higher energy than that of the external magnetic field alone because the induced magnetic dipole opposes the external field. If however the new external field strength is lower, the new induced rotation is in the reverse sense,  creating a magnetic dipole that is aligned with the magnetic field, increasing the energy in the system again as work is done.

Another aspect of this property is that the rotation-induced magnetic field contains energy, so the rotation must have inertial properties - see the paper on electromagnetic inertia here. In other words the electron picks up induced rotational angular momentum, whose value is proportional to its spin and therefore to the strength of the external magnetic field. It therefore also has a gyroscopic moment.

But the most interesting point of all is that a charged particle interacts with a magnetic field in a magnetic way. Since the only way we know of a particle’s magnetic field is by virtue of its magnetic interactions, the obvious question is “Is this the source of the electron’s dipole?” It is not possible to induce a magnetic monopole from an electric field, any more than it is possible to induce an electric monopole from a magnetic field. This structural model of the electron is compatible with the absence of magnetic monopoles in the universe.

But what about the neutron - it has no electric field but it still has a magnetic dipole - how could this be induced? If the electric field of an electron or proton followed the inverse square law all the way to zero radius the mass/energy in them would be infinite (those interested can look up “Classical electron radius” on the web for background) so at some point there must be an inner boundary to the field of these particles. The neutron may not only have this internal boundary, but could also have an external boundary at sub-nanometer radius, with a radial electric field flowing from the outer to the inner. This would give an induced magnetic dipole with no measurable external electric field. However, I have to acknowledge that this concept is rather fanciful.

So from this section we take forward the concepts that...

A charged particle in a magnetic field (or equivalently an electron moving through an electric field, the motion inducing a magnetic field) ...

• rotates at a determinate frequency
• has an induced magnetic dipole
• has angular momentum
• has a gyroscopic moment

Electrostatic attraction

Finally no picture of the electron’s electric field would be complete without mentioning its behaviour in an external electric field. The negatively- charged electron will simply be drawn towards a positively- charged electric pole. The detailed maths are here.

Electrostatic inertia

An electrostatic field has inertia - review the maths here. The structure of a magnetic dipole is such that it is very likely to lead to anisotropic inertia. The electron’s momentum is isotropic - that is, it is the same in all directions under all conditions, implying that a magnetic dipole does not contribute to the inertia in any way.

We take forward from this section that...

• there is no intrinsic magnetic dipole, just the induced one.

Work in progress - more to come