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

Question

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?

Robert · Accepted Answer

According to ampere’ law, the closed line integral of the magnetic field multiplied by the length of the 
curve is equal to the sum of the enclosed currents times the permeability of free space. 
The equation is expressed as follows:
The value of current enclosed in terms of current density is,

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....

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