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In the past, representations of electric fields in textbooks were almost always depictions of field lines, a representation that can be extremely powerful when applied to Gauss’s law and the concept of divergence. But students run into problems if this is the only representation in their mental toolbox when they attempt to understand electric fields as the gradients of potentials or when they study electromagnetic waves. What, exactly, is waving? The former emphasis on field lines arose in large part because static graphs of arrows in three-dimensional space may appear as an overlapping indistinguishable mess. Now, with the aid of modern computer graphics in a program such as Maple or Mathematica, students can rotate a graph with a simple sweep of the mouse. This engages the part of the brain that processes the visualization of objects in space and the image immediately takes on a three-dimensional effect.

Also include visualization of divergence and curl.

• Visualizing Divergence
• Visualizing Curl