I just had a pretty neat problem on my Electrodynamics (course text) mid-term. The problem is to solve for the electric field for two charged conducting spheres of different radii connected by a conducting filament so they reach the same potential.
The result (pdf of full solution) is that the electric field is greater near the surface of the smaller sphere even though it carries less of the total charge. The physical implications of this is that the electric field will be high near the parts of a charged conductor that have a small radius of curvature (ie corners). That's why you get arcing and sparking on forks and crumpled aluminum foil that you put in the microwave.
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