You can use the superposition principle to combine solutions obtained by separation of v...

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 V₀; 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, . . . V₆. In this way, using Ex. 3.4 and Prob. 3.15, find the potential inside a rectangular pipe with two facing sides (x = ±b) at potential V0, a third (y = a) at V₁, and the last (at y = 0) grounded.

Reference prob 3.16

Reference prob 3.15

Reference example 3.4

Two infinitely-long grounded metal plates, again at y = 0 and y = a, are connected at x = ±b by metal strips maintained at a constant potential V₀, as shown in Fig. 3.20 (a thin layer of insulation at each corner prevents them from shorting out). Find the potential inside the resulting rectangular pipe.