ps10

# ps10 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of...

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Problem Set 10 p. 1 of 7 MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Fall 2008 Label with your name, table number and group. Turn in at the homework box. Problem Set 10 Due: Thursday, November 13 th at 12:00 pm Warm Up Problem 1: EMF Due to a Time-Varying Magnetic Field A long narrow coil is surrounded by a short wide coil as shown in the figure at the right. The short wide coil has a diameter d S , n S turns per unit length, and a length S . It has its ends connected through a resistor of resistance R . The long narrow inner coil has a diameter d L , n L turns per unit length, and a length L . It has its ends connected across a variable power source. For each of the partial sentences below, indicate whether they are correctly completed by the phrase greater than (>), less than (<), or the same as (=). If you cannot determine which is the case from the information given, indicate not sufficient information (NSI). The current through the inner coil is increased from 0 to1 Amps over a period of 10 seconds in a smooth fashion according to the rule I L ( t ) = (0.01 A/ 2 s ) 2 t . a. The magnitude of the current in the long narrow coil at time t = 5 s is __________ the current in that coil at time t = 1 s. b. The magnitude of the current in the short wide coil at time t = 5 s is __________ the current in that coil at time t = 1 s. c. The magnitude of the current in the long narrow coil at time t = 1 s is __________ the current in the short wide coil at that same time. d. If the long narrow coil was compressed to half its length before the current was turned on, the current in the short wide coil would be __________ it was without the compression.

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Problem Set 10 p. 2 of 7 Problem 2: Superconducting Magnets Frequently to make strong, uniform magnetic fields a superconducting solenoid is used. Once current is “loaded” into the solenoid, the two ends can be tied together (we’ll look at how this is done in next weeks problem set) and then the current will continue to circulate forever. Calculate the inductance of and total energy stored (when fully charged) in the following two magnets: a) The strongest constant field laboratory magnets currently available create a field of 45 T with a current of 150 A. They have a bore diameter of 5 cm and an active length (where the field is basically uniform) of about 10 cm. b) An MRI magnet is 2 m long, 0.75 m in diameter and has a field strength of 4 T when charged to 100 A. In designing MRI magnets, people work very hard to make the field uniform throughout the core of the magnet (that is to say, it’s not just a straight solenoid). Sample Exam Problems… 3: Inductor An inductor consists of two very thin conducting cylindrical shells, one of radius a and one of radius b , both of length h .
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ps10 - MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of...

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