hw0 - Phys 3327 Fall 10 HW 0 Due Monday in lecture Homework...

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Phys 3327 Fall ’10 HW 0 Due Monday 08/30/10 in lecture Homework 0 Warm-ups Ex 1.1: Thomson’s Jumping Ring In class you saw a demonstration of ‘Thomson’s jumping ring’: A conducting ring placed around the upper half of a solenoid was propelled upwards once the solenoid was connected to AC power (see figure with coordinates labelled). a) Draw the magnetic fields lines produced by the solenoid when the current in the solenoid is non-zero. b) Let the magnetic field be B ( r, z, t ) = B ( r, z ) sin( ωt ) and assume the ring has radius a and zero resistance. Use Faraday’s law and the Lorentz force law to derive an expression for the force acting on the ring at any time t (you need not find B ( r, z ) explicitly). Deduce that there is always an upwards force on the ring. c) Extra Challenge: What happens if the ring has a non-zero resistance? Hint: Divide the magnetic field into radial and axial components. Keep in mind that the ring has an inductance!
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