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Problem Set 10

# Problem Set 10 - 8.02 MASSACHUSETTS INSTITUTE OF TECHNOLOGY...

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY Department of Physics 8.02 Fall 2007 Turn in at your table during class labeled with your name and group (e.g. L02 11C) Problem Set 10 Due: Wednesday, November 14 th at class beginning (before 10:15/12:15) This problem set focuses on material from weeks 9 & 10 (classes 21 – 24). Textbook references can be found at the top of the summaries from these days. 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 to 0.1 Amps over a period of 10 seconds in a smooth fashion according to the rule I L ( t ) = (0.01 A/s) t . a. The magnitude of the current in the short wide coil at time t = 1 s is __________ the current in that coil at time t = 5 s. b. The magnitude of the current in the long narrow coil at time t = 1 s is __________ the current in that coil at time t = 5 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. PS08 Sample Exam p. 1

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Approximations, Real World Problems, Back of the Envelope Calculations… Problem 2: MRI Magnet A standard MRI magnet is 2 m long, 0.75 m in diameter and has a field strength of 2 T. Let’s assume its just an ideal solenoid (it’s not – they work very hard to get a uniform field by arranging additional coils just in the right places). a) If it takes 100 A to make the 2 T field, what is the inductance of the solenoid? The magnet is superconducting, so is charged using the method pictured at right. A battery ε is used to drive current through leads (resistance R L = 0.5 Ω on each lead) down into the solenoid (inductance L ). All of the wires below the two leads (the resistors), including the coil, are superconducting, except for a small piece of wire connected in parallel with the coil, which is heated above its superconducting transition temperature to give it a resistance R PCS = 10 Ω (PCS stands for persistent current switch). Although I’ve drawn a battery, we really use a current supply to “charge” (or energize) the magnet, which can theoretically supply whatever voltage is necessary to get you the current you want. The current is slowly ramped upward until it reaches its desired value. Why slowly?
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