Chapter%208 - Chapter 8 The Steady Magnetic Field Dr. Ray...

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Dr. Ray Chen© Chapter 8 The Steady Magnetic Field
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Dr. Ray Chen© 8.1 Biot-Savart Law Fig. 8.1 3 12 12 1 1 2 12 12 1 1 2 4 4 R R L d I R a ˆ L d I dH R π v v v × = × =
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Dr. Ray Chen© 8.1 Biot-Savart Law have we 0, S d J i.e. 0, J if satisfied be may condition this and zero, is surface closed any crossing current the If S = = v v ∫∫ × = = 2 4 H d H R a ˆ L Id R π v v r
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Dr. Ray Chen© 8.1 Biot-Savart Law Example 1: Find the magnetic field H at point 2 due to the existence of an infinite line of current flowing along z axis r 2 r 1 dL I x z P2( ρ ,0,0)
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Dr. Ray Chen© 8.1 Biot-Savart Law r 2 r 1 dL I x z P2( ρ ,0,0) Solution to Example 1: 2 2 12 1 2 12 z a ˆ z a ˆ a a ˆ z a ˆ r r R z z + = = = ρ v v v v () 2 3 2 2 2 4 , / z z z z z a ˆ z a ˆ a ˆ z Id dH a ˆ a ˆ a ˆ a ˆ z d L d + × = = × = π φ v πρ a ˆ z z a ˆ I z a ˆ z d I H d H / 2 I 4 4 2 2 2 2 3 2 2 2 = + = + = = v v
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Dr. Ray Chen© 8.1 Biot-Savart Law Example 2: Find the magnetic field at P of a finite current element as shown in the figure y z x α 1 α 2 P(0,y,z) I
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Dr. Ray Chen© 8.1 Biot-Savart Law y z x α 1 α 2 P(0,y,z) I Solution to Example 2: z - z y 0 1 0 0 a a a b b b a a a a a a b a 4 Law Savart - Biot to According z y x z y x z y x z y x 2 12 12 = = × × = ˆ ˆ ˆ ˆ ˆ ˆ r a ˆ L Id H d v v v v π () 2 3 2 2 2 3 2 2 y 4 0 0 y 4 ) z - z 0 1 0 0 / / ) z z ( ) , , y ( z Id ) z z ( , y , ( ) , , ( z Id H d + = + × = v P point at a is which , a - is direction The φ x ˆ ˆ
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Dr. Ray Chen© 8.1 Biot-Savart Law () 2 3 2 2 4 H d P, point at y Let / ) z z ( a ˆ z d I + = = ρ π φ v y z x α 1 α 2 P(0,y,z) I Solution to Example 2 (continued): θ d sec d cos cos d ) sin( sin d cos cos ) , tan 2 2 2 1 cos sin d( dtan z - z Let = = = = = α πρ a ˆ ) sin (sin I d cos a ˆ I d sec sec a ˆ I tan d sec a ˆ I H / = = = + = 2 1 2 1 1 2 3 2 2 3 2 2 2 2 4 4 4 4 v a ˆ I , 2 H 2 , 2 infinity, is
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Chapter%208 - Chapter 8 The Steady Magnetic Field Dr. Ray...

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