c251_11 - north pole and a south pole. Physically, this...

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1 1 Example: Magnetic Field in a Solenoid Fields tend to cancel in region right between wires. •Field Lines continue down center of cylinder •Field is negligible directly outside of the cylinder I H I H 2 H L I solenoid) finite for length) unit per turns ( ( I L N H nI H LnI HL n LnI I HL l d H enc = = = = r r Example: what field is produced in an air core solenoid with 20 turns per cm carrying a current of 5A? 3 Toroidal Solenoid a 2 NI H NI a 2 H NI I a 2 H l d H enc π = = = = r r torus of center along Field a 4 • Similar to electric flux density vector D , we define the magnetic flux density vector B , in free space H B o r r μ = Units: Webers/m 2 (Wb/m 2 ) or Tesla (T) μ o = constant = permeability of free space = 4 π x 10 -7 H/m Magnetic Flux Density: B
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2 5 H B o r r μ = Magnetic Flux Density: B Magnetic Flux Ψ The magnetic flux crossing an open surface S is given by θ ψ cos B A B S B 2 . perp l . = = = r r For uniform field: . ∫∫ ∫∫ = = S . perp S dA B S d B r r Wb Wb/m 2 6 0 . = = ∫∫ S S d B r r Closed Surface S Net Flux crossing S: Reason: It is impossible to separate the north pole from the south pole in a magnet. No matter how small the magnet is divided, it always has a
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Unformatted text preview: north pole and a south pole. Physically, this means that magnetic charges (monopoles) do not exist. Magnetic Flux Density: B Magnet 7 . = = ∫∫ S S d B r r Closed Surface S Net Flux crossing S: From the Divergence Theorem dV . V B . S d B S r r r ∫∫∫ ∫∫ ∇ = . = ∇ B r The B-field is solenoidal , i.e. the divergence of the B-field is identically equal to zero. Magnetic Flux Density: B 8 Maxwell’s Equations for Electrostatic and Magnetostatic Fields J H x E x B . D . v r r r r = ∇ = ∇ = ∇ = ∇ ρ ∫∫ ∫ ∫ ∫∫ ∫∫ ∫∫∫ = = = = = = S L L S encl S S d . J d . H d . E S d . B Q dV S d . D encl V v I l l r r r r r r r r r v Gauss’s Law Non-Existence of magnetic monopole Conservative property of E-static Ampere’s Law Differential Integral Remarks Form Form...
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This note was uploaded on 07/11/2011 for the course ELEC 251 taught by Professor Lynch during the Spring '10 term at Concordia Canada.

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c251_11 - north pole and a south pole. Physically, this...

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