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pdes for electrostatics & heat flow 453Figure 17.7 Left: Computed equipotential surfaces and electric field lines for a realisticcapacitor. Right: Equipotential surfaces and electric field lines mapped onto the surface for a3-D capacitor constructed from two tori (see OpenDX in Appendix C).Figure 17.8 Left: The geometry of a capacitor formed by placing two long, square cylinderswithin each other. Right: The geometry of a capacitor formed by placing two long, circularcylinders within each other. The cylinders are cracked on the side so that wires can enter theregion.4. Thinking outside the box⊙: Find the electric potential for all points outsidethe charge-free square shown in Figure 17.1. Is your solution unique?17.10 Unit II. Finite-Element Method ⊙In this unit we solve a simpler problem than the one in Unit I (1-D rather than 2-D),but we do it with a less simple algorithm (finite element). Our usual approach to PDEsin this text uses finite differences to approximate various derivatives in terms of thefinite differences of a function evaluated upon a fixed grid. The finite-element method−101COPYRIGHT 2008, PRINCET O N UNIVE R S I T Y P R E S SEVALUATION COPY ONLY. NOT FOR USE IN COURSES.ALLpup_06.04 — 2008/2/15 — Page 453