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Unformatted text preview: Prof. David R. Jackson ECE Dept. Spring 2011 Notes 26 ECE 2317 ECE 2317 Applied Electricity and Magnetism Applied Electricity and Magnetism 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 ( 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 Magnetic Gauss Law Magnetic Gauss Law x y z B S (closed surface) N Magnetic pole (not possible) ! ˆ S B n ds ⋅ = ∫ Ñ N S S No net flux out ! Magnetic Gauss Law: Differential Form Magnetic Gauss Law: Differential Form ˆ S B n dS ⋅ = ∫ Ñ B ∇ ⋅ = From the definition of divergence we then have 1 ˆ lim V S div B B n dS V ∆ → ≡ ⋅ ∆ ∫ Ñ Hence Ampere’s Law Ampere’s Law y x Iron filings $ [ ] 7 2 4 10 H/m I B φ μ πρ μ π = ⋅ = × I (exact value) Experimental law: 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 = × = 2 I B φ μ πρ = ⋅ 1 [ A ] current produces: Hence [ ] 7 4 10 H/m μ π = × [ ] [ ] [ ] ( 29 7 1 A 2 10 T 2 1 m μ π × = ⋅ so Ampere’s Law (cont.) Ampere’s Law (cont.) Define: 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) B H μ = Hence Ampere’s Law (cont.) Ampere’s Law (cont.) $ ( 29 $ ( 29 ( 29 2 2 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 ⋅ = ⋅ + + = = = = = ∫ ∫...
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This note was uploaded on 08/05/2011 for the course ECE 2317 taught by Professor Staff during the Spring '08 term at University of Houston.
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