Problem
A toroid has a rectangular cross section. Show that the self-inductance is
where is the total number of turns and , , and are shown above. [Hint: Use Ampère’s law to get as a function of inside the toroid, and integrate.]
Solution
Magnetic field inside as a function of :
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the self-inductance is related to the flux is the integral of the magnetic field over a cross-section of the toroid.