Visualizing an Electric Field With HTML5 and WebGL, Part 4: An Infinite Charged Plane

 Another classic charge distribution is the infinite charged plane, or infinite sheet of charge. It generates a particularly simple electric field normal to the plane, and a number of interesting models can be produced by combining planes or planes and point charges.

A positively charged plane.

The infinite charged plane is presented as a finite rectangle for practical reasons. Drawing a small section of the plane reduces hardware requirements, especially for mobile devices. Consider trying to draw all the field lines for an infinite sheet.

A charged plane is constructed by specifying the charge density, σ, the density of field lines per unit charge, ρ, and the four corners of the rectangular area of the plane that will be drawn (x0, y0, z0), (x1, y1, z1), (x2, y2, z2), and (x3, y3, z3). In any given diagram, each charged plane is a transformation of a unit rectangle into the given position. This means that no matter how many rectangles are drawn, the same four vertices are used over and over to draw them.

Focus on clarity. This is a large charge distribution and the electric field is strongly directional. Orient them so the configuration and shape of the field is clear. Choose a field line density that produces enough field lines to illustrate the physics, but not so many that the visualization is difficult to interpret. The parallel plates are a subtle example, the initial position is inclined slightly so that the presence of two oppositely charged planes is clear.

The simplest example is the single charged plane. Even in this case the plane is inclined to clearly show the field extending in both directions normal to the plane. It is also clear that the field is uniform and does not fall off with distance as does the field from a point charge. As a side note, in the early testing of this diagram, because of a typo I generated over 25,000 field lines and crashed the JavaScript engine. It pays to exercise a bit of caution.

Two oppositely charged planes.

The next example of two oppositely charged planes generates a strong electric field between the planes, but beyond them the fields cancel. This is expected from the superposition principle. This configuration also serves as a gateway into discussing capacitance and energy density in an electric field. In this illustration, the field line density, ρ, on one of the planes is set to zero to generate a cleaner representation.

A negative charge above a negatively charged plane.

This next example is a showcase for this visualization technique. A negative charge placed above a negatively charged plane deflects the field in a way that is much easier to understand when rotated and viewed from multiple angles. For an interesting example of symmetry in physics consider what you would expect if the sign of both the charged plane and the the point charge were reversed.

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