Amperes Circuital Law states that the line integral of the magnetic field H around a closed path equals the total current enclosed.
∫ H dl ∑ I
Applying this to the special case of a circular path around a single current carrying conductor allows a simple calculation to be made to determine H at a radius r from the wire:
Similar analyses may be applied to other examples that lend themselves to a closed form integration. More complicated examples usually involve computer solution.Fortunately, many practical cases exist where a simple calculation is possible. We will only be concerned with these cases.
H.dl around a closed path containing thoseN turns will be equal to NI.First suppose we have a coil of N turns carrying a current I. Then the integral of