ASSIGN_3 - Assignment #3 PHYSICS 354/4-01 ELECTRICITY &...

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Assignment #3 PHYSICS 354/4-01 ELECTRICITY & MAGNETISM II March 2010 Assignment #3, Page 1 of 2 B 1 () w/2,w/2,0 x z l I Solution to Assignment # 3 246 . 5.33, p Express the dipole field in terms of m and r . + = q q q p m ˆ sin ˆ cos 2 4 3 3 r m r r m B o dip for r >> dimension of dipole. q is measured from the m axis. q ˆ can be written in terms of r m ˆ and ˆ , q q q q q q q sin ˆ ˆ ) 90 cos( ˆ ) (cos ˆ ˆ ˆ ) ˆ ˆ ( ˆ ) ˆ ˆ ( ˆ - - = + ° - = + = r m r m m r r m m . ( 29 ( 29 m r r m r m r m r r m r m r m r r m B o o o - = - = + - + = ˆ ) ˆ 3 ( 4 ˆ ˆ 3 4 sin ˆ ˆ sin ˆ 2 4 3 3 3 3 3 p m q p m q q q q p m 246 . 5.36, p The problem here is to find the magnetic dipole moment of a spinning charged spherical shell. The shell can be considered as a stack of rings. A typical ring located at q contributes q q sw w p q q p s q p d R Rd R T q dI R z m d sin ) / 2 ( ) sin 2 ( where , ) sin ( ) ( ˆ 2 2 = = = = ( 29 p p p p q q q swp q q q q q p q q 0 3 4 0 2 4 0 3 4 2 0 2 3 ˆ ) )( 1 ( ˆ sin ˆ ) sin ( sin ˆ ˆ - - = - - = = = = = R z d R z d R z R d R z dm z m = + - + - - = 3 1 1 3 1 1 ˆ 4 R z z R ˆ 3 4 4 wp s ( 29 r r R r r z R r r z R R r r r m A o o o o × = × = × = ×
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This note was uploaded on 12/15/2010 for the course PHYS 354 taught by Professor Josephshin during the Winter '10 term at Concordia Canada.

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ASSIGN_3 - Assignment #3 PHYSICS 354/4-01 ELECTRICITY &...

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