Introduction to Electrodynamics · Problem 5.19

Magnetostatics — David J. Griffiths

Physics · amperian-loop-surface-independence

Problem

In calculating the current enclosed by an Amperian loop, one must, in general, evaluate an integral of the form Ienc=∫SJ⋅da.I_{\text{enc}} = \int_S \mathbf{J} \cdot d\mathbf{a}. The trouble is, there are infinitely many surfaces that share the same boundary line. Which one are we supposed to use?

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