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notes26 2317 - ECE 2317 ECE Applied Electricity and...

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Prof. David R. Jackson ECE Dept. Spring 2011 Notes 26 ECE 2317 ECE 2317 Applied Electricity and Magnetism Applied Electricity and Magnetism
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Magnetic Field Magnetic Field Lorentz Force Law: In general, (with both E and B present): F qv B = × ( 29 F q E v B = + × This experimental law defines the magnetic flux density vector B . The units of B are Webers/ m 2 or Tesla [ T ]. ε r N N v q S N N S
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( 29 F q v B = × Beam of electrons moving in a circle, due to the presence of a magnetic field. Purple light is emitted along the electron path, due to the electrons colliding with gas molecules in the bulb. (From Wikipedia) Magnetic Field (cont.) Magnetic Field (cont.) v × × × × × × × × × × × × × × × × F
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Magnetic Gauss Law Magnetic Gauss Law x y z B S (closed surface) N Magnetic pole (not possible) ! ˆ 0 S B n ds = Ñ N S S No net flux out !
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Magnetic Gauss Law: Differential Form Magnetic Gauss Law: Differential Form ˆ 0 S B n dS = Ñ 0 B ∇⋅ = From the definition of divergence we then have 0 1 ˆ lim V S div B B n dS V Ñ Hence
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Ampere’s Law Ampere’s Law y x Iron filings $ [ ] 0 7 0 2 4 10 H/m I B φ μ πρ μ π - = = × I (exact value) Experimental law:
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Ampere’s Law (cont.) Ampere’s Law (cont.) Note: The definition of the Amp is as follows: [ ] [ ] 7 2 10 T at 1 m B φ ρ - = × = 0 2 I B φ μ πρ = 1 [ A ] current produces: Hence [ ] 7 0 4 10 H/m μ π - = × [ ] [ ] [ ] ( 29 7 0 1 A 2 10 T 2 1 m μ π - × = so
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Ampere’s Law (cont.) Ampere’s Law (cont.) Define: 0 1 H B μ $ [ ] A/m 2 I H φ πρ = The units of H are [ A/m ]. H is called the “magnetic field” (for single infinite wire) 0 B H μ = Hence
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Ampere’s Law (cont.) Ampere’s Law (cont.) $ ( 29 $ ( 29 ( 29 2 0 2 0 ˆ ˆ 2 2 2 2 C C C H dr H d d z dz H d I d I I d I φ φ π π φ φ ρ φ ρ ρ ρ φ ρ φ πρ φ π π π = + + = = = = = Ñ Ñ Ñ y x I C A current (wire) is inside a closed path.
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0 0 2 0 C I H dr d φ π = = Ñ y x I C A current (wire) is outside a closed path.
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