Electron in magnetic field and cathode ray tube

[arul_k]

If the motion of an electron creats a magnetic field around it then why is an electron beam in a cathode ray tube deflected at right angles and not towards the magnetic field?

Also, what would be the effect of a magnetic field on a stationary (relative to the field)electron?

 

[Dale]

The force on an electron is described by the Lorentz force law:
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfor.html#c2

It is always proportional to and perpendicular to both the velocity and magnetic field, so the force is 0 for a stationary electron.

 

[arul_k]

The force on an electron is described by the Lorentz force law:
http://hyperphysics.phy-astr.gsu.edu/hbase/magnetic/magfor.html#c2

I am aware of the Lorentz force law, as I mentioned in the question I know the electron deflects at right angles to the magnetic field.

But since the electron in motion generates a magnetic field why is the deflection not towards the magnetic field (just as a magnet would behave under the influence of a magnetic field)?

 

[Dale]

You never consider a particle's own field. Neither the particle's own electric nor own magnetic field affect its motion. Essentially, fields don't push on fields, they push on particles. If at a given point in space there are two fields they simply superimpose, there is no force at that point in space due to the superposition.

 

[technician]

If you take a practical view you find that electrons flowing along a wire (an electric current) produce a magnetic field around the wire (Right hand grip rule for direction).
When this wire is placed in a magnetic field (between the poles of a magnet) It experiences a force in certain circumstances.
Flemings left hand rule gives the directions of current, magnetic field and resulting force.
I free electron moving with a velocity experiences the same force but the electron is not constrained by the wire and can follow a circular path.
Experimental evidence shows what happens

 

[vanhees71]

Of course, it's wrong to say that a particle's own electromagnetic field has no effect to it. This is in fact a quite difficult problem that came up with the discovery of point-like charged particles like the electron at the end of the 19th century.

At this time, Lorentz has developed a classical theory for the motion of such particles in a electromagnetic field. Of course, he knew that the acceleration of such a point particle means that electromagnetic waves, the particle's wave field, are created, which carry energy and momentum away from the particle, which thus must feel a force corresponding to this energy-momentum flow.

The trouble with this, however, is that the total energy and momentum are infinite for a point particle. However, this is already true for a charge at rest. The em. field of a charge at rest is the Coulomb field (with vanishing magnetic-field components as expected from electrostatics), which has an infinite energy, but it doesn't radiate any em. waves. Also according to the principle of relativity a point charge in constant motion doesn't radiate wave fields. That's why there's one closed solution for a free point charge, which runs with constant velocity and produces a Lorentz-boosted Coulomb field (with both electric and magnetic components).

Lorentz came only to a partial solution of the problem of a charge in general (accelerated) motion: He solved the equation of motion for the particle in the given (external) electromagnetic field, neglecting the radiation reaction completely. Then he treated the radiation reaction as a perturbation, where he could subtract an infinite amount of energy, which he interpreted as (part of the) electromagnetic mass of the point charge. That was the first "renormalization" of an infinite "self energy" for an electron (in 1916, i.e., long before the analogous problem in quantum electrodynamics has been solved by Schwinger, Feynman, Tomonaga, and Dyson in ~1948-1950).

The best treatment of these problems in classical electrodynamics can be found in

F. Rohrlich, Classical Charged Particles, World Scientific.

 

[Dale]

This thread is more than 4 years old. However, in the intervening time I probably would have answered more like vanhees71 did than my post from '07.

Basically, you cannot completely consistently treat charged point particles in classical electrodynamics.

 

[Philip Wood]

But since the electron in motion generates a magnetic field why is the deflection not towards the magnetic field (just as a magnet would behave under the influence of a magnetic field)?

To behave (roughly) like a magnet, the electron needs to be following a circular (or, at least, closed) path.