Why Right Angles?

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In summary, the left-hand motor rule tells us what will happen when we run a current in a magnetic field. The right-hand generator rule tells us what voltages and currents will occur. Interesting is that the current itself creates a local magnetic field. Why the right-angledness? It is an observed and accepted property of magnetics. The only other place I know of where this behaviour is observed is with my ancient to gyroscope.f
  • #1
We have the left-hand (motor) rule. We know exactly what happens when we run a current in a magnetic field.

Its reversible! The right hand (generator) rule tells us what voltages and currents occur when we move the conductor in a magnetic field. Interesting we have to do work to get it done if we happen to be running a current. Interesting too that the current itself makes a field around the wire that locally modifies the original field.

Why the right-angledness? Is this addressed anywhere, or is it just an observed and accepted property?

The only other place I know where I have seen relentless "act perpendicular" behavior is with my (ancient) to gyroscope. Maybe the electric / magnetic properties are also somehow associated with something spinning.

  • #2
It need not always be a right angle, but the sin of the angle between the directions. For example, in the Fleming's left hand rule, the force is equal to the product of the current and the direction of the magnetic filed times the sine of the angle between the latter two. It is actually a cross product. The direction of the force is given by the left hand rule, that is in the direction of the thumb, even if the angle between the I and B is not a right angle.
  • #3
Hi Shooting Star

I confess I was really asking after something more fundamental!

I had used the famous search engine, and read what I could find on this. Clearly force is maximum when the current is at at right angles to the field, and at any other angle, only the component remaining will count. An engineering model rule. This is why generator windings make sinusoidal outputs when rotated in a linear field.

The engineers have already gamed the phenomenon to the point they can provide fine design information that very accurately models the effect. The right-angledness is a assumed physical property of magnetics, and electrics, and the associated force effects. For me, the more important observation is that the motion force is exactly at right angles to the plane of the field and current components.

Very closely associated, I think, is light and other frequency radiation. Before anyone says "photon" and "quantum" and "Maxwell", I already think the fact that making a time-varying electric field will produce a time-varying magnetic field at right angles!,and vice versa, is also just so interesting. It is very likely part of the same game, despite that no mechanical force is involved!
Even though the resulting (wave?) then zooms away at a uniquely interesting speed that occupies much of this forum space, the key thing I point to is that the direction is mutually perpendicular.

Even when we miss out the motion (generator) component, and physically restrain the conductors, and make a structure that forcibly sets boundary conditions on the fields so we store the energy in magnetic materials (a transformer), we have invoke the flux linkage concepts that admirably respect these cross product quantities.

We have lots of excellent mathematical modelling that preserve the right-angled axioms, and I fully respect the work that sets it out. I was just asking ... "What is it about the nature of so much we try to describe that somehow automatically ends up with this right-angled behavior property"?

Quite naturally, we would wonder if they are somehow tied together. Could a thing like the Left-Hand Motor Rule, Maxwell's Equations relating to electromagnetic fields, and a mechanical gyroscope all be displaying these right-angled cross-product behaviours, because they ultimately all involve something spinning?
  • #4
(Reposting – not much modification)

One of your questions is if these behaviours are all involved to something spinning. You yourself have perhaps put a finger on it in your last paragraph, by noticing the similarity of gyroscopes and motors.

Keeping things very simple and without invoking higher dimensions etc, when a mass loop spins, there is angular momentum, and when a current loop spins, there is a magnetic field. The common thing is that in both cases, there is a plane of rotation, and there is only one straight line which is normal to the plane. In these cases, you get your right angles because of spinning indeed.

This goes at least a wee bit toward answering your question why there are right angles and cross products in both the cases. Many phenomena with right angles can perhaps be linked ultimately to such geometrical pictures. Of course, this has nothing to do with the question why angular momentum should exist, apart from the way we already think about it. I have not touched on the EM wave.

(On a slightly related note, when it was first discovered that an electron had an intrinsic magnetic moment, this was ascribed to some sort of intrinsic “spin” of the electron.)

If you would elaborate on your question a bit more…

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