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Unformatted text preview: Chapter 37 Maxwell’s Equations 324 37 Maxwell’s Equations In this chapter, the plan is to summarize much of what we know about electricity and magnetism in a manner similar to the way in which James Clerk Maxwell summarized what was known about electricity and magnetism near the end of the nineteenth century. Maxwell not only organized and summarized what was known, but he added to the knowledge. From his work, we have a set of equations known as Maxwell’s Equations. His work culminated in the discovery that light is electromagnetic waves. In building up to a presentation of Maxwell’s Equations, I first want to revisit ideas we encountered in chapter 20 and I want to start that revisit by introducing an easy way of relating the direction in which light is traveling to the directions of the electric and magnetic fields that are the light. Recall the idea that a charged particle moving in a stationary magnetic field experiences a force given by B F h h h × = P v q This force, by the way, is called the Lorentz Force . For the case depicted above, by the right- hand rule for the cross product of two vectors, this force would be directed out of the page. B P v q B P v q F Chapter 37 Maxwell’s Equations 325 Viewing the exact same situation from the reference frame in which the charged particle is at rest we see a magnetic field moving sideways (with velocity P v v h h − = ) through the particle. Since we have changed nothing but our viewpoint, the particle is experiencing the same force. We introduce a “middleman” by adopting the attitude that the moving magnetic field doesn’t really exert a force on the charged particle, rather it causes an electric field which does that. For the force to be accounted for by this middleman electric field, the latter must be in the direction of the force. The existence of light indicates that the electric field is caused to exist whether or not there is a charged particle for it to exert a force on. The bottom line is that wherever you have a magnetic field vector moving sideways through space you have an electric field vector, and, the direction of the velocity of the magnetic field vector is consistent with direction of v h = direction of B E h h × . You arrive at the same result for the case of an electric field moving sideways through space. (Recall that in chapter 20, we discussed the fact that an electric field moving sideways through space causes a magnetic field.) The purpose of this brief review of material from chapter 20 was to arrive at the result direction of v h = direction of B E h h × . This direction relation will come in handy in our discussion of two of the four equations known as Maxwell’s Equations....
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