Introduction to Electrodynamics · Problem 3.42

Potentials — David J. Griffiths

Physics · separation-of-variables-superposition

Problem

You can use the superposition principle to combine solutions obtained by separation of variables. For example, in Prob. 3.16 you found the potential inside a cubical box, if five faces are grounded and the sixth is at a constant potential V0V_0; by a six-fold superposition of the result, you could obtain the potential inside a cube with the faces maintained at specified constant voltages V1,V2,…V6V_1, V_2, \ldots V_6. In this way, using Ex. 3.4 and Prob. 3.15, find the potential inside a rectangular pipe with two facing sides (x=±bx = \pm b) at potential V0V_0, a third (y=ay = a) at V1V_1, and the last (at y=0y = 0) grounded.

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