Chapter 4 Fields of Stationary Electric Charges: III Capacitance of An isolated Conductor Capacitance btwn TWo Conductors Potential Energy of a Charge Distribution Energy density in an Electric Field Forces on conductors
Chapter 4 Fields of Stationary Electric Charges : III ◼ Capacitance of An Isolated Conductor ◼ Capacitance btwn Two Conductors ◼ Potential Energy of a Charge Distribution ◼ Energy Density in an Electric Field ◼ Forces on Conductors
4.1 Capacitance of an isolated conductor Consider an isolated conductor, either carrying charges or not We know that the potential v on the conductor is always a constant Both experiments and theory show that, as charge is added to it, its potential rises The magnitude of the change in potential is the amount of charge added and depends on the geomet rical configuration of the conductor as well. This fact can be sum marized as C is called the capacitance of the conductor
Remarks (1) The physical meaning of C is the amount of charge needed to rise the potential by a unit(volt). In SI unit, C has the unit farad coulomb I farad U0 (2)Although C has been defined to be Q/V, it actually depends only on the size and shape of the conductor Example 1. isolated spherical conductor of radius R If it has a charge Q on it, then the potential is 4丌∈ 0 so the capacitance is given by C=Q/V=4丌oR
4.2 Capacitance btwn two conductors Note that an isolated conductor certain restrictions (1)In reality, a conductor is always under influence of the environment So it's difficult to isolate a conductor (2 )An isolated conductor has a small C. For instance a conductor of the size of the earth r=64×10°m, C=4丌0R=7×10 4 F Thus, we need capacitors consisting of two conductors
Example 1. Parallel-plate capacitor(see Fig 4-2) Each of the two plates has an area a and the spacing bwtn them is s One carries a charge @, the other carries-Q So the field btwn is E=F=Eoa and the potential difference is V=Es the capacitance is 02 Say, A=(50 M)2, s=0.1mM, then C X 10+ F. It's greater than that of the earth