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Unformatted text preview: Scott Hughes 24 February 2004 Massachusetts Institute of Technology Department of Physics 8.022 Spring 2004 Lecture 6: Capacitance 6.1 Capacitance Suppose that I have two chunks of metal. A charge + Q is on one of these chunks,- Q is on the other (so that the system is neutral overall). Each chunk will be at some constant potential. What is the potential difference between the two chunks of metal? +Q-Q 2 1 + + + + + +------ Whatever the potential difference V 2- 1 =- R 2 1 ~ E d~s turns out to be, it must of course turns out to be independent of the integration path. In fact, as we can show with a little thought, the potential difference V must be proportional to the geometry. This means that the potential difference (or voltage) between the two chunks must take the form V = (Horribly messy constant depending on geometry) Q . The horrible mess that appears in this proportionality law depends only on geometry. In other words, it will depend on the size and shape of the two metal chunks, their relative orientation, and their separation. It does not depend on their charge. This constant is defined as 1 /C , where C is the Capacitance of this system. A system like this is then called a capacitor . The 1 / may seem a bit wierd; the point is that one usually writes the capacitance formula in a different way: we put Q = CV . A key thing to bear in mind when using this formula is that Q refers to the charge separation of the system. In other words, when I say that a capacitor is charged up to some level Q , Figure 1: Q = CV . I mean that I have put + Q on one part of the capacitor,- Q on the other. The capacitor as a whole remains neutral!! I emphasize this now because I often find students are some-...
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