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Electomagnetic Induction

1. Imagine a superconductor in its normal state in the shape of a ring immersed in a magnetic field parallel to the central axis (that is, perpendicular to the plane of the ring.) Suppose the ring is cooled and becomes superconducting.
(a) Describe what happens to the field
(b) If the ring is pulled parpendicularly out of the field, what will happen to the flux in the hole in the "doughnut"?
(c) Account for the energy associated with the work done on the ring (if any) in yanking it from the field region.

2. An electron is orbiting between the poles of an electromagnet in a device called a betatron. The field is gradually being increased. How does the machine accelerate the electron? What keeps it in orbit?

Multiple choice:

1. If you have a horizontal length of copper wire moving across a horizontal magnetic field. There will be: (a) a negative voltage induced across its ends (b) a positive voltage induced across its ends (c) no voltage induced across its ends (d) a time-varying voltage induced across it ends (e) none of these. Explain your choice.

2. A closed loop moves at a constant speed parallel to a long straight current-carrying wire: (a) the induced current in the loop will progress clockwise (b) there will be no induced current in the loop (c) the induced current in the loop will progress counterclockwise (d) the induced current in the loop will vary with the speed at which the loop moves (e) none of these. Explain your choice.

3. The more rapidly a magnet approaches a coil the:
(a) lower the current in the coil (b) greater the resistance of the coil (c) greater the induced voltage across the coil (d) more it is attracted (e) none of these. Explain your choice.

Problem

1. A uniform magnetic field of 100 mT passes perpendicularly through a loop of wire having an area of 0.021 m^2. In 0.002 0 s the loop is rotated so that it is parallel to the field. What is the average time rate0of-change of flux through the loop?

2. A 100-turn of wire is removed laterally from an axial B-field in 20 ms, and an emf of 1.0 V is induced across it in the process. How big was the field if the cross-sectional area of the coil is 4.0 cm^2?

3. A coil of 100 turns is penetrated by a flux of 0.050 Wb in 0.021 s. Determine the numerical value of the average induced emf.

Solution Preview

QUESTIONS:
<br>(1) (a) There will be zero magnetic field inside the ring, because superconductors have B=0 inside them (The so called "Meisner" effect")
<br>(b) The magnetic field lines will try to avoid the superconducting region. However there are surface currents present at the surface of the superconducting ring that establish B=0 inside it. When moving the ring, the ring will enter a region of B=0, the magnetic field lines become relaxed (the currents are reduced) and the intensity of the field lines becomes less, when the ring is completely removed from the region, the intensity of magnetic flux becomes equal to its initial value. So by moving the ring out, we ...

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