An exact solution for the capacitance of a three plate system is obtained and is used to quantify the error made by the inverse sum rule. Three finite, parallel disks are arranged as two capacitors in series. By treating the system as an electrostatic boundary value problem, exact solutions for the potential and capacitance are derived for the total system and for each pair of plates. The inverse sum rule is then applied to the two constituent capacitors and compared to the exact solution for the total system. Also provided are analyses of the equal plate charge hypothesis typically assumed for series capacitors, relations for the coefficients of capacitance for the system, a capacitive maximum, repulsive plate forces, charge migration on the inner plate, and plots of the field lines for the three plate system.

Topics
Electrostatics, Electromigration
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© 2002 American Association of Physics Teachers.
2002
American Association of Physics Teachers
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