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lec05 - Scott Hughes Massachusetts Institute of Technology...

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Scott Hughes 15 February 2005 Massachusetts Institute of Technology Department of Physics 8.022 Spring 2005 Lecture 5: Fields and potentials around conductors The electrostatic uniqueness theorem 5.1 Conductors For much of the rest of this class, we will be concerned with processes that involve conductors : materials in which it is easy for charges to move around. We will discuss conductors in some depth when we discuss currents; for now, we will just summarize a few of their properties. Among the best conductors are metals — silver, gold, copper, aluminum, etc. The atoms of these metals form a crystalline structure in which electrons can easily hop around from atom to atom. Although a chunk of metal is neutral overall, we can visualize it as being made of lots of positive charges that are nailed in place, paired up with lots of negative charges (electrons) that are free to move around. In isolation, the negative charges will sit close to the positive charges, so that the metal is not only neutral overall, but also largely neutral everywhere (no local excess of positive or negative charge). Under the influence of some external field, the electrons are free to move around. Some materials conduct OK, but are not as good as metals. For example, salty water has lots of charges that are free to move around under the influence of an ~ E field. However, since these charges — usually sodium and chlorine ions — are far more massive than an electron, and they do not flow in a crystaline structure, salty water is not a very high quality conductor. Another example is graphite: the somewhat unusual bond structure of graphite makes it a fairly good conductor, but only in certain directions. At the opposite end of the spectrum are insulators : materials in which the electrons are bound quite tightly to the constituent molecules and hence have essentially no freedom to move. Insulators are typically made from organic materials such as rubber or plastic, or from crystals formed from strong covalently bounded molecules, such as quartz or glass. The effectiveness of a substance as a conductor is quantified by its resistivity , a number that expresses how well it resists the flow of current. We will revisit this quantity in about a week when we discuss currents in detail; for now, suffice to say that small resisitivity means a good conductor. In SI units, resistivity is measured in “Ohm-meters” (usually written Ω-m); in cgs units, resistivity turns out to be measured in seconds. Here are a few example values: 46
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Material Resistivity (Ω-m) Resistivity (sec) Silver 1 . 6 × 10 - 8 1 . 8 × 10 - 17 Copper 1 . 7 × 10 - 8 1 . 9 × 10 - 17 Gold 2 . 4 × 10 - 8 2 . 6 × 10 - 17 Iron 1 . 0 × 10 - 7 1 . 1 × 10 - 16 Sea water 0 . 2 2 . 2 × 10 - 10 Polyethylene 2 . 0 × 10 11 220 Glass 10 12 10 3 Fused quartz 7 . 5 × 10 17 8 . 3 × 10 8 As you can see, the resistivity of ordinary materials varies over an enormous range, reflecting the very different electronic properties of materials around us.
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