Assignment 01

# Assignment 01 - falling loop c If you want to prevent the...

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Electromagnetic Theory, PHYS 441B Norbert L¨utkenhaus Due: Wednesday, 21. Jan 2009, 10:30 80 Points Assignment 1 Remark: All known results from situations in Electrostatics and Mag- netostatics can be used in without derivation in assignments and exams. Problem 1: Loop in magnetic and gravitational Feld 50 P Consider a rigid, conducting, square loop of mass m and resistance R which sits partially in a time dependent homogeneous magnetic Feld B ( t ) and underlys the gravitational forces under standard lab conditions. The width of the loop be b , the hight within the magnetic Feld be l ( t ). Initially, no current ﬂows in the loop and we can assume to be able to work in the quasistatic regime. Neglect e±ects of self-inductance. a) what forces act on the loop? Write down the total force acting on the loop as a function of B ( t )and l ( t ). b) Assume that B ( t )= B 0 is constant in time. Assume also that l ( t =0) is initially suﬃciently large. What is the steady state velocity of the

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Unformatted text preview: falling loop? c) If you want to prevent the loop from falling, consider the following questions in the qualitative sense: Do you have to decrease or increase the Feld in time? Will you be able to hold the loop in equilibrium for an arbitrary amount of time? (Give reasons!) d) Now to the quantitative answer: Calculate the magnetic Feld B ( t ) which steadies the loop and indicate the range of validity for the solu-tion. 1 Problem 2: Self-inductance (Griﬃth Problem 7.27, p. 316) 30 P Try to compute the self-inductance of the ’hairpin’ loop shown below. (Neglect the contribution from the ends; most of the ﬂux comes from the long straight section.) You’ll run into a snag that is characteristic of many self-inductance calculations. To get a deFnite answer, assume the wire has a tiny radius ± , and ignore any ﬂux through the wire itself. 2...
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Assignment 01 - falling loop c If you want to prevent the...

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