Chapter 3.4, Problem 3.42P

You can use the superposition principle to combine solutionsobtained by separation of variables. For example, in Prob. 3.16 you found thepotential inside a cubical box, if five faces are grounded and the sixth is at a constant potential $V_0;$ by a six-fold superposition of the result, you could obtain thepotential inside a cube with the faces maintained at specified constant voltages $V_1,V_2,\mathrm{...}{V}_6$ . In this way,using Ex. 3.4 and Prob. 3.15, find the potential inside arectangular pipe with two facing sides $\left(x=\pm b\right)$ at potential $V_0$ , a third $\left(y=a\right)$ at $V_1$ , and the last (at $y=0$ ) grounded.