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Electromagnetic Induction: Flux, EMF and Mutual Inductance

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Please help me with the attached problem. There are two pages to the problem, having parts A-E.

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Solution Summary

A current carrying wire induces EMF in a loop between a fixed pair of rails and moving straight wire. Five different parts are solved step by step and explained.

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(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 ...

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