The iron core of an electromagnet is a torus (doughnut shape body) of circular cross-section of 1 cm diameter and circular center line of 10 cm diameter. The relative permeability of the core material is 100. The magnet is excited by 100 turns of DC current wound around the core. A 1 mm air gap is cut in the core, perpendicular to the axis.
What is the current required to produce a field of 0.2 tesla in the gap?
In your calculations assume that the magnetic field is distributed uniformly in the cross-section of the core, and neglect the effects of fringing fields in the gap.
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The technique to solve this problem is to use the Magnetic Circuits Approach, ie, we have MMFs analogous to voltage sources, reluctance's of the toroid and air gap equivalent to resistances, and the flux analogous to current.
So we basically have two ...
This solution illustrates how the Magnetic Circuits Approach can be used and constructs the response in a step-by-step manner with explanations.