Electromagnetic Induction: Flux, EMF and Mutual Inductance

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Answer:

(a) According to ampere's law the line ingral of the magnetic field through a colsed loop is mu not times the sum of the current in the loop. mathematically

where the left hand side is giving the line integral of the magnetic field and I is the total current through the loop.

Consider an imaginaty loop of radius r with the current carrying wire at the center the magnitude of the field B is constant everywhere on the loop and the direction of the field is parallel to the loop hence the line integral is given ...