Problem 19P

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

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

Step 1 of 1

We are suppose to find which surface are we going to use in evaluating the current enclosed by an Amperian loop as there are infinitely many surfaces.

For a field ( ) which is divergence-less it implies that is independent of surface, for any given boundary line.

Now, is divergence-less which it is for a steady current.

Therefore, we can use any surface to evaluate the current enclosed by an Amperian loop.