Conceptual Understanding in Introductory Physics XVI: Superposition Arguments

Superposition is a powerful principle in physics, especially in introductory electromagnetic theory. A charged particle’s electric field exists independently of the fields of any other particles. A thorough understanding of superposition can prevent the frequent misunderstanding that fields can somehow be “blocked,” which is subtly different from saying that the net field at a point can be zero. In other cases, superposition can help in calculating the net field of continuous sources. Superposition is closely related to symmetry in that both can be used to justify certain geometric properties of fields, as the following questions illustrate.

(a) Using superposition (no numbers, no mathematical symbols), explain why the electric field of a uniformly charged, infinitely large, planar charge distribution must be perpendicular to the plane. Using a similar argument, explain why the electric field’s magnitude must be independent of distance from the plane.

(b) Construct a similar line of reasoning for the electric field of an infinitely long, uniformly charged linear charged distribution.

The concept of solid angle may make the first question easier to tackle, but solid angle is rarely mentioned in the introductory course. I’ll have a question about this in a future post.

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