Engineering and Applied Sciences Applied Physics 216 Lecture 6: Lecture 6
21 Feb 2017
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Ap 216 lecture 6 more potential theory, capacitance, forces on conductors, For n conductors each at potential vi (no free charges) x. Diagonal c"s are called capacities and off diagonal ones are coefficients of inductance. Note cij is symmetric, can solve for vi if you know the qj"s. Note cij only depend on geometry of conductors. C has an inverse (cij)-1 called the potential matrix p so. 1 p q q ij i j (4) (5) Capacitance measures energy storage ability of system of voltage biased conductors. But j(x ) is just the potential at x due to the jth body at potential vj and all other bodies at. Note the other bodies are important in determining (x ) but only through their effect on g. Best to treat electric and magnetic forces together. With einstein convention summing over repeated indices we have. E m ijk klm il jm im jl (9) (10) (11) (12) (13)
