Posted: Jun 22, 2010 3:31 pm
by Farsight
Visualizing a slice through a cylindrical electromagnetic field

Look at the right-hand rule on English wikipedia. For a current in a wire, your thumb points in the direction of the current flow, and your fingers “are curled to match the curvature and direction of the motion or the magnetic field”.

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But note it’s one field, it’s the electromagnetic field, not separate electric fields and magnetic fields. Maxwell knew it, Minkowski knew it, and Oleg jefimenko knew it. Jefimenko's equations are a useful reminder in this respect.

Jefimenko wrote:"...neither Maxwell's equations nor their solutions indicate an existence of causal links between electric and magnetic fields. Therefore, we must conclude that an electromagnetic field is a dual entity always having an electric and a magnetic component simultaneously created by their common sources: time-variable electric charges and currents."


The electromagnetic field is a dual entity, there’s only one field there. Moving through an electric field doesn’t cause a magnetic field to be generated, because as Minkowski said, it’s the field, and it exerts force in two ways. What does it look like? It doesn’t actually look like anything, but iron filings on a piece of paper tells you that you can visualize a field, even if it's just a flat slice through it. And to visualise the complete electromagnetic field, you need a drill bit or a reamer:

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If I look at it from the top it reminds me of an electric vector field, like this one from Andrew Duffy’s PY106 physics course material at http://physics.bu.edu/~duffy/ :

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When I then look at the rotational magnetic vector lines of the right-hand-rule, I'm searching for a combined visualisation. So I grab a reamer in my right fist, put my left thumb on the bottom of it, and push upwards. It turns. I'm emulating the right-hand rule for the current in the wire. The reamer is giving an analogy of the cylindrical electromagnetic field around a vertical column of electrons. Pushing upwards is emulating the current flow, and the rotation I can feel is the magnetic curl or rot. The current flows, and the result is rotation, as demonstrated by Faraday way back in 1844:

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See this NASA electromagnetism page for a little more history. Minkowski referred to a wrench and Maxwell referred to a screw because the electromagnetic field really is like this. It’s essentially a “twist” field. Motion through it results in “turn”. Or vice-versa. Start with forward motion like with a pump-action screwdriver, and you get rotation, turn. Turn a screw with a screwdriver and the twist results in forward motion, so you can induce a current up the wire. This is why we have dynamos and generators, because this is how the electromagnetic field is. It's a "twist/turn field", as borne out by the physical evidence of say galactic jets, where two streams of charged particles moving at different velocities spiral around each other. The magnetic field is the "turn" aspect of this, that's why we talk of curl or rot. Because rot is short for rotor, and it really makes things turn:

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The reamer depicts the electromagnetic field for a column of electrons, at an imaginary cylindrical surface some distance round the wire. You have to use a fatter reamer to visualize the electromagnetic field for a larger cylindrical surface. Then to match the way the field diminishes with distance, the degree of twist has to reduce. So imagine a continuous series of fatter and fatter reamers, all occupying the same space, all with the twist diminishing. Now take a horizontal slice through this set of reamers. You’re also taking a horizontal slice through an electron’s electromagnetic field, and it's going to be something like this:

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That’s what the electron’s electromagnetic field would "look like" if you sliced through it from any direction. Let your eyes linger on it. It looks rather like a vortex, but at the heart of it is an electron. The electron is the vortex. That's was Maxwell's mistake. The vortex is in the particle, not in the intervening space. If only he'd got that right or somebody had fixed it! A slice through the electromagnetic field looks spiral because it combines the radial electric field lines with the concentric magnetic field lines.