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Lorentz Force Special Rel Paradox and Stored Energy

This week I've been reading about the apparent paradox [1]between the Lorentz force law, (the law that explains how an electric charge is affected by a magnetic field), and special relativity reported last year.  In the article describing the paradox [2], I came across the phrase 'hidden momentum'.  I hadn't heard this term in relation to electromagnetism before, (neither had some of my professors), so I embarked on a little research project to learn more about it.  As an aside, if anyone would like to comment with a high level overview of the 'hidden momentum' concept, it would be greatly appreciated, (Thanks!)

Stored Energy
The first thing we need to know is that electric and magnetic fields store energy.  Put very basically, electric charges would rather rearrange so that an object is electrically neutral, and magnetic fields would rather not change.  Changing either a distribution of charges, or a magnetic field requires energy and the energy used to make the change winds up being stored in the new charge distribution or magnetic field.  One of the most impressive examples of energy being stored in a electric charge distribution is the Van de Graaff generator.  Charge is moved via a moving belt onto a large metal sphere.  It's just a big version of the same process that takes place when you rub your feet on the carpet and then generate a spark when you touch a door knob.  The energy used to move the charge is stored in the electric field created by the charge.  When enough energy is stored, it can all be released quickly creating a spark:

The picture above is from the Van de Graaff generator at the Boston Science Museum.  If you ever get a change, go!  It's awesome, and my high school classmate works there, (yeah, I'm proud!)

As I said, energy can also be stored in a magnetic field.  An example of this can be found in the ignition coils used in cars[3].  Electric energy (relatively), slowly creates a magnetic field that stores the energy.  The original magnetic field is then forced to rapidly collapse.  This collapse releases the stored energy very quickly.  The resulting pulse of energy is used to create the spark that ignites the gas in the cars engine.

That's all for today!  More tomorrow.

1.  Popular science press on the special relativity paradox and its resolution

2.  The actual paradox article:

3.  Induction Coils on Wikipedia


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