29b - MasteringPhysics: Assignment Print View 04/19/2007...

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04/19/2007 02:22 PM MasteringPhysics: Assignment Print View Page 1 of 5 http://session.masteringphysics.com/myct/assignmentPrint?assignmentID=1064960 [ Assignment View ] E ð lisfræ ð i 2, vor 2007 29b. Electromagnetic Induction 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. Displacement Current and Ampere-Maxwell Law The Ampère-Maxwell Law Learning Goal: To show that displacement current is necessary to make Ampère's law consistent for a charging capacitor Ampère's law relates the line integral of the magnetic field around a closed loop to the total current passing through that loop. This law was extended by Maxwell to include a new type of "current" that is due to changing electric fields: . The first term on the right-hand side, , describes the effects of the usual electric current due to moving charge. In this problem, that current is designated as usual. The second term, , is called the displacement current ; it was recognized as necessary by Maxwell. His motivation was largely to make Ampère's law symmetric with Faraday's law of induction when the electric fields and magnetic fields are reversed. By calling for the production of a magnetic field due to a change in electric field, this law lays the groundwork for electromagnetic waves in which a changing magnetic field generates an electric field whose change, in turn, sustains the magnetic field. We will discuss these issues later. (Incidentally, a third type of "current," called magnetizing current, should also be added to account for the presence of changing magnetic materials, but it will be neglected, as it has been in the equation above.) The purpose of this problem is to consider a classic illustration of the need for the additional displacement current term in Ampère's law. Consider the problem of finding the magnetic field that loops around just outside the circular plate of a charging capacitor. The cone-shaped surface shown in the figure has a current passing through it, so Ampère's law indicates a finite value for the field integral around this loop. However, a slightly different surface bordered by the same loop passes through the center of the capacitor, where there is no current due to moving charge. To get the same loop integral independent of the surface it must be true that either a current or an increasing electric field that passes through the Ampèrean surface will generate a looping magnetic field around its edge. The objective of this example is to introduce the displacement current, show how to calculate it, and then to show that the displacement current is identical to the conduction current . Assume that the capacitor has plate area and an electric field between the plates. Take
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This note was uploaded on 02/28/2010 for the course PHYS 1554 taught by Professor Donald during the Spring '10 term at UNBC.

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29b - MasteringPhysics: Assignment Print View 04/19/2007...

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