Discussion
Match the arrangement with its capacitance.
1. Parallel plates 2. Coaxial cylinders 3. Isolated sphere
P. \( 4\pi\epsilon a \) Q. \( \epsilon A/d \) R. \( 2\pi\epsilon/\ln(b/a) \) per unit length
Answer: A
The three formulae correspond to the three symmetries and to the three ways the field falls off with distance. Recognising which geometry a problem presents settles which expression to reach for, and each may be derived in a line from the appropriate Gaussian surface.
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