Recall from Lecture 4 the goals of our discussion
Goal 1: To establish a viable model for characterizing information flow along a wire.
Goal 2: To establish some important electrical concepts.Our discuss of signal propagation on a wire in the previous lecture was seriously limited: in particular, we did not include the effects of magnetism which is a serious oversight! We should have realized that something wasn't right if we had thought about the possibility of an inertial effect in our earlier Hydraulic model of a wired channel -- an RC transmission line. The inertia effect - the mass of the liquid - would tend to keep in the liquid in motion!
A introduction to basic ideas about magnetism can be found at NASA's The Exploration of the Earth's Magnetosphere web site. Particularly relevant to our dicussion is the elementary discussion entitled Magnetic Fields.
Of profound importance is the famous 1820 experiment of Hans Christian Oersted that establishing the fundamental connection between magnetism and electricity. It is valuable to read Oersted's own account of that experiment in an insightful paper by Professor Frederick Gregory of the Department of History at the University of Florida.
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Hans Christian Ørsted (1777 - 1851) Biographies
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Question: What did Oersted find? Answer: That electric current flow produces magnetic force or a force on magnet. But there there are strange characteristics of this force! From antiquity there has been a reasonably clear notion about the directional characteristics of an electric force -- two charges either attract or repel each other. Oersted found that the directional characteristics of the magnetic force are quite different from those of the electric force.
To gain further insight in to magnetism see:
- A movie which displays the relationship between the direction of current flow and the direction of the magnetic field.
- Two wonderful applets from Molecular Expressions - i.e.
Of course, this discovery of "electromagnetism" provided the practical "missing link" which enabled the the electric telegraph to flourish -- viz.,there was now means for practical detection of electrical signals. In nineteenth century terms, many possibilities emerge quite rapidly. One of the first classes of semi-successful implementations were the rather weird "needle telegraphs." But a key invention was the electromagnet (see Joseph Henry's contribution) which was the enabling technology for the Morse-Vail-Henry electromagnetic telegraph.
But the story is not yet complete. In particular, how do we complete the following picture?
Michael Faraday (1791-1867)
Joseph Henry (1797-1878)
The Crucial Experiments sSource"Between 1821, when he invented his rotator, and 1831, Faraday was too busy with other matters to give much attention to electromagnetism. In August of 1831, however, he undertook experiments to test some notions he had about the nature of electricity. He rejected the idea that electricity consisted of a fluid or a stream of particles, but the action of his rotator convinced him that something must move through a wire. Some experiments on sound suggested to Faraday that electricity might consist of vibrations moving through matter.Using a Magnet
"If this were so, Faraday reasoned, perhaps he could cause the vibrations in one current-carrying wire to set up similar vibrations in a nearby, but separate, wire. Thinking that these vibrations might be intensified by acting through an electromagnet, he made one out of an iron ring wrapped with wire on one side. On the other side of the ring, he wrapped another coil of wire, which he attached to a galvanometer (simply a compass with a wire connected). When, on August 29th 1831, he connected the first side of the ring to a battery, he was watching the galvanometer needle - it jumped, then returned to normal. On disconnecting the battery, the needle jumped again. By starting or stopping a current in the first wire, he had induced, for an instant, a current in the second wire. Faraday had made a great discovery, but it was only the beginning of his work, not the end.
"Faraday quickly realized that his ring experiment not only supported his notions about electricity, but it also revealed something about the relationship between electricity and magnetism. Faraday embarked on a series of experiments to further clarify this relationship. The most important of these was with a paper cylinder wound with several coils of copper wire, connected to a galvanometer. When Faraday thrust a bar magnet into the hollow of the cylinder, the meter's needle jumped, then when he pulled the magnet out, he needle jumped again, but in the opposite direction. Induction did not require the creation of a magnet (as in the ring experiment), but was caused simply by moving a magnet near a wire. This was truly, in Faraday's words, 'the production of electricity from magnetism.' ...." (Source)
Again see three wonderful applets from Molecular Expressions - i.e.
Hydraulic analogy for electromagnetic induction:Energy storage in fluid flow II: Suppose that there a subsidiary fluid storage tank (a pressurizer) to the pipe (Sketch of energy storage element). It is pretty obvious that the pressurizer tends to keep the flow going if the pump stops or fluctuates.Why do we say that electromagnetic induction adds an inertial effect?
Let us derive the resonance condition: (reference)
The induced voltage across the inductor
and the stored voltage across the capacitor
With S1 closed and S2 open
However, after openning S1 and closing S2 at t = 0
Making the equation homogeneous in the current
Comparing this equation with equations studied in our discussion of harmonic oscillators, we see that the circuit is a harmonic oscillator with resonance frequency ; note that the effective restoring constant is 1/C and the effective inertia constant is L.