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notes25 2317

# notes25 2317 - Magnetic Field ECE 2317 Applied Electricity...

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Prof. Filippo Capolino ECE Dept. Fall 2006 Notes 25 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) Magnetic Field Magnetic Field ε r Lorenz Force Law: N S v q In general, (with both E and B present): F qv B ( ) Fq E v B =+ × This experimental law defines the magnetic flux density vector B . The units of B are Webers/m 2 or Tesla [T]. Magnetic Gauss Law Magnetic Gauss Law x y z B S (closed surface) N Magnetic pole (not possible) ! ± 0 S Bnd s ⋅= v N S S No net flux out ! Magnetic Gauss Law: Differential Form Magnetic Gauss Law: Differential Form ± 0 S S v 0 B ∇⋅ = Apply the divergence theorem: () 0 V BdV ∇⋅ = Since this applies for any volume,

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Ampere Ampere ’s Law s Law y x Iron filings ± [] 0 7 0 2 41 0 H / m I B φμ πρ μπ =⋅ I (exact value) Ampere Ampere ’s Law (cont.) s Law (cont.) Note: the definition of one Amp is as follows: [ ] 7 21 0 T at 1 m B φ ρ = () 0 7 0 2 1A 0 T 21m I B μ π ×= 1 [A] current produces: So [ ] 7 0 0 H / m Ampere Ampere ’s Law (cont.) s Law (cont.) Define: 0 0 1 HB BH = = ± A/m 2 I H = The units of H are [A/m]. H is called the “magnetic field” (for single infinite wire) Ampere Ampere ’s Law (cont.) s Law (cont.) y x I ± ± l ( ) 2 0 2 0 2 2 22 CC C Hd r H d d zd z I d II d I φφ ρφ φπ ππ ⋅= + + = ⎛⎞ = ⎜⎟ ⎝⎠ == = ∫∫ ± vv v C The current is inside a closed path.
0 0 2 0 C I H dr d φ π ⋅= = ∫∫ v y x I C The current is outside a closed path.

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notes25 2317 - Magnetic Field ECE 2317 Applied Electricity...

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