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Electro-Magnetic Induction

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A rectangular conducting loop of width w, height h, and resistance R is mounted vertically on a nonconducting cart (see attachment). The cart is placed on the inclined portion of a track and released from rest at position P1 at a height y above the horizontal portion of the track. It rolls with negligible friction down the incline and through a uniform magnetic field B in the region above the horizontal portion of the track. The conducting loop is in the plane of the page, and the magnetic field is directed into the page. The loop passes completely through the field with a negligible change in speed. Express your answer in terms of the given quantities and fundamental constants.

a.) Determine the speed of the cart when it reaches the horizontal portion of the track.

b.) Determine the following for the time at which the cart is at position P2, with one-third of the loop in the magnetic field.
i. The magnitude of the emf induced in the conducting loop
ii. The magnitude of the current induced in the conducting loop.

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Solution Preview

a) At the height y, potential energy of the cart = mgy where m = mass of the cart & loop

As the cart reaches the level track, it potential energy is completely converted into kinetic energy. ...

Solution Summary

Step-by-step solution discusses electro-magnetic induction.