30 - http:/session.masteringphysics.com/myct 04/19/2007...

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http://session.masteringphysics.com/myct Page 1 of 15 http://session.masteringphysics.com/myct [ Assignment View ] E ð lisfræ ð i 2, vor 2007 30. Inductance Assignment is due at 2:00am on Wednesday, March 14, 2007 Credit for problems submitted late will decrease to 0% after the deadline has passed. The wrong answer penalty is 2% per part. Multiple choice questions are penalized as described in the online help. The unopened hint bonus is 2% per part. You are allowed 4 attempts per answer. Mutual Inductance Mutual Inductance of a Double Solenoid Learning Goal: To learn about mutual inductance from an example of a long solenoid with two windings. To illustrate the calculation of mutual inductance it is helpful to consider the specific example of two solenoids that are wound on a common cylinder. We will take the cylinder to have radius and length . Assume that the solenoid is much longer than its radius, so that its field can be determined from Ampère's law throughout its entire length: . We will consider the field that arises from solenoid 1, which has turns per unit length. The magnetic field due to solenoid 1 passes (entirely, in this case) through solenoid 2, which has turns per unit length. Any change in magnetic flux from the field generated by solenoid 1 induces an EMF in solenoid 2 through Faraday's law of induction, . Part A Consider first the generation of the magnetic field by the current in solenoid 1. Within the solenoid (sufficiently far from its ends), what is the magnitude of the magnetic field due to this current? Express in terms of , variables given in the introduction, and relevant constants. ANSWER: = Answer not displayed Part B Part not displayed Part C Part not displayed Part D Part not displayed Part E Part not displayed Part F Part not displayed Self Inductance Self-Inductance of a Solenoid Learning Goal: To learn about self-inductance from the example of a long solenoid. To explain self-inductance, it is helpful to consider the specific example of a long solenoid, as shown in the figure. This solenoid has only one winding, and so the EMF induced by its changing current appears across the solenoid itself. This contrasts with mutual inductance, where this voltage appears across a second coil wound on the same cylinder as the first. Assume that the solenoid has radius , length along the z axis, and is wound with turns per unit length so that the total number of turns is equal to . Assume that the solenoid is much longer than its radius. As the current through the solenoid changes, the resulting magnetic flux through the solenoid will also change, and an electromotive force will be generated across the solenoid according to Faraday's law of induction: . Faraday's law implies the following relation between the self-induced EMF across the solenoid and the current passing through it:
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This note was uploaded on 11/02/2009 for the course MASTERING PHYS taught by Professor All during the Spring '09 term at Kettering.

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30 - http:/session.masteringphysics.com/myct 04/19/2007...

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