electromagnetism - Math 21a Supplement on Electricity and...

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Math 21a Supplement on Electricity and Magnetism Vector fields on R 3 play a central role in Maxwell’s theory of electricity and magnetism. In particular, the electric field in space is described in Maxwell’s theory by a vector valued function of space and time, E (t, x). This vector provides the direction and magnitude of the electric field at any given point and at any given time. Likewise, the magnetic field is also described in Maxwell’s theory by a vector valued function of space and time, B (t, x). (Why not the letter ‘M’ for magnetic field? I am not sure. In any event, the traditional letter is ‘B’.) Maxwell proposed a set of equations which he postulated constrain the possible vector valued function pairs ( E , B ) which can arise as real world electric and magnetic fields. These are the famous Maxwell equations. (Actually, various portions of these equations were written down by others prior to Maxwell’s culminating contribution.) These equations involve the operations of curl and divergence in a fundamental way. In any event, here are Maxwell’s equations in a vacuum (no charged, polarizable or magnetically susceptible materials or particles present): div E = 0, div B = 0, t E = curl B , t B = - curl E . (1) Here, I have written these equations in units where various natural constants (such as the speed of light) are equal to 1. In a physics book, these equations generally appear with various natural constants whose values depend on the particular choice of units of measurement.
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This note was uploaded on 02/18/2012 for the course MATH 310 taught by Professor Gregoryj.galloway during the Fall '11 term at University of Miami.

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electromagnetism - Math 21a Supplement on Electricity and...

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