Question

381. (4 points) In calculating the steady current enclosed by an Amperian loop, one must, in general, evaluate an integral of the form Ienc= ∫s J · da, where S is the surface area. The trouble is that there are infinitely many surfaces that sharethe same boundary line. Which one are we supposed to use?

Answer 1

Answer:

You can chose any surface that shares the same boundary line as per theorem of divergence less for stead currents

Step-by-step explanation:

For constant and steady currents the current density field has no divergence,

which can be shown:

                                        ∀. J = 0

The theorem 2 states that fields with no divergence has an integral as:

                                         $\int\limits^S_S {F.} \, ds$

Which makes in independent of the surface of integration provided that the surfaces share the same boundary. Hence, you can pick any surface as long as the above condition is validated.