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Physics at Hamilton |
This is an outline of the material that I hope to cover in this course. I have also assembled a very tentative schedule that may give some idea of how we shall work our way through this material. The schedule will be modified as the semester progresses.
In Electromagnetism I hope to cover
This should start as a review and then develop the idea of the electric potential.
We shall skim quickly through this chapter, which deals with the interactions of the electric field with solid matter. We shall concentrate on the ideas of the P and D fields and upon the boundary conditions that apply at the junctions between two different materials or between a material and the vacuum.
We shall concentrate on sections 1, 2, and 5 and will make use of computers to find electric fields in all but the simplest configurations.
Moving electric charges form a current and currents generate magnetic fields. We shall explore how different current distributions lead to different shapes of magnetic field. We shall cover all the un-starred sections.
This is a more advanced topic and we shall probably omit this chapter.
Just as moving charges generate magnetic fields, so changing magnetic fields generate electric fields. This chapter will explore these ideas which lie at the heart of modern civilization since they allow us to build power plants that convert mechanical energy into electric energy to run our world.
This completes the set of fundamental equations that describe Electromagnetism and puts them into their final form. This formulation follows the 9th Century work of James Clerk Maxwell, which predicts electromagnetic radiation and so paves the way for technologies from radio to TV and modern cell phones.
We shall study how electromagnetic energy can propagate through empty space and through non-conducting materials and shall see why you can't get good radio reception in a submarine.
Every time an electric charge accelerates it generates EM radiation. We shall look at some simple situations and see how shaking the electric field leads to EM waves in much same way that shaking one end of a rope generates mechanical waves.
We can bring our understanding of the EM field into the 20th Century by re-examining Einstein's Special Theory of Relativity. We shall see how the single idea of the electric charge leads to all of the phenomena of electromagnetism once we understand how to correctly transform from one reference frame to another.
In labs I hope to also use material from chapters 7 and 8 which explore interactions of charges and metal conductors. This will lead us to some understanding of the electronic circuits that fill our modern world.
To support all of these physical explorations we shall use materials from the Advanced Mathematics book. In particular we shall use
The electric and magnetic fields are examples of vector fields and so we shall need to study the mathematics that describe such fields. We shall explore the world of Div, Grad, Curl, and all that.
The simpler, older way to describe vector fields is in terms of integrals over the fields. These integrals are somewhat less useful for computing fields in practice but extremely important for understanding the geometrical meaning of Maxwell's equations. We shall use most of the material from this chapter.
Just as Newton's laws of motion lead to ordinary differential equations to describe all but the simplest kinds of motion, so the methods of Vector Analysis applied to Maxwell's equations lead to partial differential equations for the electric and magnetic fields. We shall use some of the material from this chapter to find solutions to Laplace's Equation, Poisson's Equation, and the Wave Equation.
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Physics at Hamilton |