HW10 - Physics 122 Spring 2009 Document #21: Tenth Homework...

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Unformatted text preview: Physics 122 Spring 2009 Document #21: Tenth Homework Assignment page 1 of 8 PHYS 122: Tenth Homework Assignment March 31, 2009 This homework due in Box outside of Rock 207: 5:00 PM Sharp, Monday April 6, 2009 Announcements: Third Hour Exam is Friday, April 10, 9:30 AM. Worth 10% of your grade. Mark your calendar now. Problem 1 starts next page... Physics 122 Spring 2009 Document #21: Tenth Homework Assignment page 2 of 8 Problem 1: (from Third Hour Exam two years ago:) x z y B(t) E(t) endcap We consider a finite region of space (shown above). This region of space contains no charge and no currents. However, there are externally applied uniform time-varying electric and magnetic fields in the region which are defined as follows: vector E ( t ) = E t 3 3 vector B ( t ) = B sin( t ) Suppose in this region we define three imaginary geometric concepts: We define a closed surface S which is a fixed cylinder that is tipped at an angle relative to y-axis as shown. The length of the cylinder is and the radius is a . We define an open surface S 1 which is the upper flat endcap of this cylinder S . We define a loop L 1 so that the loop L 1 bounds the open surface S 1 . In other words the loop corresponds to the circumference around the endcap. Part (a): Determine the total flux of the the externally applied electric field as a function of time through the surface S . Explain how you got your answer. Part (b) : Determine the total flux of the the externally applied magnetic field as a function of time through the surface S . Explain how you got your answer. Part (c) : Determine the total flux of the the externally applied magnetic field as a function of time through the surface S 1 . Explain how you got your answer. Physics 122 Spring 2009 Document #21: Tenth Homework Assignment page 3 of 8 Part (d) : Determine the induced voltage as a function of time around the loop L 1 . Explain how you got your answer. Part (e) : Determine the magnitude of the induced magnetic field on the loop L 1 that results from the associated displacement current. Hint: there is no real current here. The displacement current is a term corresponding to a change in the flux of electric field through a surface. Explain how you got your answer....
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This note was uploaded on 11/06/2009 for the course PHYS 122 taught by Professor Covault during the Spring '08 term at Case Western.

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HW10 - Physics 122 Spring 2009 Document #21: Tenth Homework...

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