“A point charge q is placed at a distance d from the center of an uncharged conducting sphere of radius R (R < d). Find the force on the charge. Verify that the force is always attractive, no matter the sign of q.”
What if it wasn’t?
Professor Ananya Rao had taught electricity and magnetism for thirty-one years. She could derive Maxwell’s equations in her sleep, calculate the magnetic field of a toroid while chopping onions, and explain Lenz’s law to a room of hungover sophomores without once checking her notes.
She’d skipped a term. A term involving the second derivative of the potential—a term that, for a perfect conductor, should cancel exactly. But her cancellation required the sphere to be infinitely conducting. Perfectly rigid in its response.
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