Assn3 - in the solenoid is turned off. Hence calculate the...

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PHY 4211 Electromagnetic theory and Optics 2010 Assignment 3 Due: Friday February 5, 2010 Do all problems, but hand in ONLY questions marked with * (e.g. Q2*) (G=Griffiths) Q1*: After I discussed G Example 8.4, one of you asked a very good question: when the charged inner and outer cylinders rotate, their surface currents should give rise to additional magnetic fields which will contribute to the EM angular momentum. Is angular momentum still conserved? (He is absolutely correct and I have left out this contribution in my class discussion.) Now you help me answer his question. (a) Suppose the current is being switched off from t = 0 to t f , and at t f when the current vanishes, the inner and outer cylinders are rotating with angular velocities a ω and b , respectively. Using cylindrical coordinates ) , , ( z R φ , find the electric and magnetic fields between the outer and inner charged cylinder after the current
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Unformatted text preview: in the solenoid is turned off. Hence calculate the EM angular momentum. (b) Calculate the extra torques on the charged cylinders when the current of the solenoid is being switched off. Calculate the extra angular momentum the cylinders gain (or lose). Is angular momentum conserved? Q2*: G Problem 8.15 (a) , p.363. Q3: G Problem 9.12 , p.382. Q4*: An EM field is described by ( ) . sin ˆ cos sin ˆ sin cos ˆ cos cos cos t y ky kx x ky kx B B z t ky kx E E − = = r r Find the relation between E and B , and the dispersion relation between k and . This field can exist inside a square metal box of dimension k / π in the x and y directions and arbitrary height. Sketch the magnetic field at 2 = t ....
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This note was uploaded on 12/10/2011 for the course PHYS 4211 taught by Professor Wkliu during the Spring '11 term at CUHK.

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