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582 appendix cFigure C.12 The visual program on the left produces the surface plot of the electric potentialon a 2-D plane containing a capacitor. The surface height and color vary in accord with thevalues of the potential.DX makes the plotting of vector fields easy by providing the module Gradientto compute the gradient of a scalar field. The visual program Laplace.net_3 on theleft in Figure C.13 produces the visualization of the capacitor’s electric field shownon the right. Here the AutoGlyph module is used to visualize the vector nature ofthe field as small vectors (glyphs), and the Isosurface module is used to plot theequipotential lines. If the 3-D surface of the potential were used in place of the lines,much of the electric field would be obstructed.C.5.5 Sample 5: 3-D Scalar PotentialsWe leave it as an exercise for you to solve Laplace’s equation for a 3-D capacitorcomposed of two concentric tori. Although the extension of the simulation from2-D to 3-D is straightforward, the extension of the visualization is not. To illustrate,instead of equipotential lines, there are now equipotential surfaces V (x, y, z), eachof which is a solid figure with other surfaces hidden within. Likewise, while we canagain use the Gradient module to compute the electric field, a display of arrowsat all points in space is messy. Such being the case, one approach is to map theelectric field onto a surface, with a display of only those vectors that are parallelor perpendicular to the surface. Typically, the surface might be an equipotentialsurface or the xy or yz plane. Because of the symmetry of the tori, the planesappear to provide the best visualization.The visual program Laplace-3d.net_1 on the left in (Figure C.14) plots an electricfield mapped onto an equipotential surface. The visualization on the right shows−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 582