assignment3 - Ans Φ m r> a = M zxa 5 5 r 5 Φ m r< a =...

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Classical Electrodynamics II Spring 2010 Prof. Hyun-Chul Kim Assignment 3: Magnetism in the presence of matter The due date for this assignment is Wednesday March 31, 2010. 1. Griffiths, Problem 6-8. 2. Griffiths, Problem 6-12. 3. Griffiths, Problem 6-13. 4. Griffiths, Problem 6-27. 5. Wangsness, Problem 20-9. 6. Wangsness, Problem 20-10. 7. Wangsness, Problem 20-12. 8. Find the magnetic scalar potential of a magnetized sphere of radius a having magnetization M ( r ) = M 0 z ˆ x . (Hint: Use the following relation Φ m ( r ) = 1 4 π · V M 0 z ˆ x | r r | = 1 4 π ∂x V z | r r | . (1) If possible, apply the Spherical harmonics.
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Unformatted text preview: [ Ans. ] Φ m ( r > a ) = M zxa 5 5 r 5 , Φ m ( r < a ) = M zx 5 . (2) 9. Starting from the force equation F = ∫ J ( r ) × B ( r ) dτ, (3) and the fact that a magnetization inside a volume V bounded by a surface S is equivalent to a volume current density J m = ∇ × M and a surface current density K m = M × ˆ n , show that in the absence of macroscopic conduction currents the total magnetic force on the body can be written F = − ∫ V ( ∇ · M ) B ext dτ + ∫ S ( M · ˆ n ) B ext da, (4) where B ext is applied the magnetic field. 1...
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This note was uploaded on 03/22/2011 for the course PHYS 425 taught by Professor Guang during the Spring '09 term at Seoul National.

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