hw8sols - MasteringPhysics 8:41 PM Assignment Display Mode...

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4/8/08 8:41 PM MasteringPhysics Page 1 of 18 http://session.masteringphysics.com/myct Assignment Display Mode: View Printable Answers Physics 202 Assignment 8 Due at 11:00pm on Wednesday, March 26, 2008 View Grading Details Magnetic Field due to Semicircular Wires Description: This problem establishes the magnetic field resulting from the current flowing in two, concentric, semicircular wires. A loop of wire is in the shape of two concentric semicircles as shown. The inner circle has radius ; the outer circle has radius . A current flows clockwise through the outer wire and counterclockwise through the inner wire. Part A What is the magnitude, , of the magnetic field at the center of the semicircles? Hint A.1 What physical principle to use Use the Biot-Savart law separately on each semicircle and on the wire segments that join the semicircles. You should then add the results. This is possible because the magnetic field is a vector field and hence it is additive. The Biot-Savart law is where is the permeability of free space and is the distance between the infinitesimal wire element and the point where the magnetic field is measured. Part A.2 Compute the field due to the inner semicircle What is the magnitude, , of the magnetic field due to the inner semicircle (of radius ) at the point P? Part A.2.a Finding the integrand Pulling the constants outside of the integral we have . What is the value of the integrand for the semicircle? Part A.2.a.i Determine the direction of the field due to any point on the inner semicircle What is the direction of this field? ANSWER: into the screen out of the screen So you don't really need to do a vector integral, since all the points contribute in the same direction. Hint A.2.a.ii The cross product Observe that is just in this case, since they are perpendicular to each other with lying along the tangent and being the radial vector. Hint A.2.a.iii The -dependence of Recall that in this case , independent of which point on the semicircle you are considering.
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4/8/08 8:41 PM MasteringPhysics Page 2 of 18 http://session.masteringphysics.com/myct Express in terms of and . ANSWER: = From the Biot-Savart law, you will need to integrate around the circumference of the inner semicircle. Part A.2.b Evaluate the integral In the last part you found that the integral simplifies to . What is over the semicircle with radius ? Hint A.2.b.i How to approach this problem This integral is nothing but the length of the circumference of the semicircle. Express your answer in terms of and standard constants. ANSWER: = Express your answer in terms of , , and . ANSWER: = Part A.3 Direction of the field due to the inner semicircle What is the direction of this field? ANSWER:
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This note was uploaded on 10/29/2008 for the course PHYS 202 taught by Professor Everett during the Fall '08 term at University of Wisconsin.

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hw8sols - MasteringPhysics 8:41 PM Assignment Display Mode...

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