Which surface to use in Ampere's law?

Question

In calculating the current enclosed by an Amperian loop, one must, in general evaluate an integral of the form

$$I_\text{encl} = \int \mathbf{J}\cdot\mathrm{d}\mathbf{a}$$

The trouble is, there are infinitely many surfaces that share the same boundary line. Which one are we supposed to use?

score 5 · Accepted Answer · answered Dec 17 '13 at 18:55

5

The identity is correct for all of the infinitely many surfaces (isn't math amazing?).

In general you either have a surface you care about in the first place or are in a position to choose the easiest surface.

answered Dec 17 '13 at 18:55

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