notes26 2317 - Biot-Savart Law ECE 2317 Applied Electricity...

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Prof. Filippo Capolino ECE Dept. Fall 2006 Notes 26 ECE 2317 ECE 2317 Applied Electricity and Magnetism Applied Electricity and Magnetism Notes prepared by the EM group, University of Houston . (used by Dr. Jackson, spring 2006) Biot Biot -Savart Law Savart Law () l 2 4 V Jr R H dV R π ′ × = l 2 4 s S H dS R ′ × = a) V J R r r b) S J s R r r Biot Biot -Savart Law (cont.) Savart Law (cont.) l 2 4 C Id R H R ′× = A Rule: C is in direction of I c) I R r C dl ´ r Example Example ± ± ± ± l l l 22 cos sin dz d z Rrr x xy y z z z z zz Rz R z ρφ ρρ ρ ′′ = =− = + =+− =− =+ = + ± A ± ± ± ± Find H l 2 4 C R H R = A x y z r R I d A
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Example (cont.) Example (cont.) () l ± ± 22 3 2 3 2 4 4 4 C zz Izd z z H z dz I z Id z z ρρ ρ πρ ρφ π φ +∞ −∞ +∞ −∞ ⎡⎤ ′ × ⎢⎥ + ⎣⎦ = + = + = + ± ± l 2 4 C R H R ′× = A x y z r R I d A Example (cont.) Example (cont.) ± ± 3 2 3 2 0 4 2 4 z H z z z +∞ −∞ +∞ = + = + ± [] A/m 2 I H ⎛⎞ = ⎜⎟ ⎝⎠ Hence: ± 2 1 2 4 I H = Note: this agrees with the answer obtained by Ampere’s law. Example Example l ± l l l ± l 2 3 2 4 ' ' ' '' 4 C C R H R da d Rz z a a R za a az I H d φφ φρ = ′′ = =+− = + =+ ×− = + A A ± ± ± v Find H x y z a R r = (0 , 0 ,z ) I d A Example (cont.) 2 3 2 A/m 2 Ia Hz = + ± l l 2 3 2 0 3 2 00 3 2 ' 4 ' 4 2 4 za z Ia Hd Ia z z d Ia Ha z ππ −− = + + = + ∫∫ ± ± ± ± l 3 2 4 C I H d = + ± x y z a R r = (0 , 0 ,z ) I d A
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magnetic materials magnetic materials Because of electron spin, atoms tend to acts as little current loops, and hence as electromagnetics, or bar magnets.
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notes26 2317 - Biot-Savart Law ECE 2317 Applied Electricity...

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