ECE-305-Lecture14

# ECE-305-Lecture14 - Engineering Electro-Magnetics...

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Engineering Electro-Magnetics Engineering Electro-Magnetics ECE-305, Lecture 14 Dennis McCaughey, Ph.D. 16 March 2010

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03/16/2010 Dennis McCaughey, ECE305, Spring 2010 2 Homework Homework 8.17 8.24 8.29 due Tues March 23
03/16/2010 Dennis McCaughey, ECE305, Spring 2010 3 Chapter 8: The Steady Magnetic Field Chapter 8: The Steady Magnetic Field Summary Of Maxwell’s Equations for static fields 0 is the magnetic field intensity in 0 v s vol s s d Q dv d Amps d I d meter d ρ = = = = = = D S E L H L J S H B S Ñ Ñ Ñ Ñ Ñ

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03/16/2010 Dennis McCaughey, ECE305, Spring 2010 4 Biot-Savart Law (Differential Form) Biot-Savart Law (Differential Form) Can not be measured physically Right-hand rule: Magnetic vector points into the paper Units of Amperes per Meter Inverse square law in distance At this point in our development we are dealing with DC currents Reminiscent of Coulomb’s Law 12 1 2 2 0 12 4 R dQ a d R πε = E The Biot-Savart law expresses the magnetic field intensity d H 2 produced by a differential current element I 1 d L 1 . The direction of d H is into the page
03/16/2010 Dennis McCaughey, ECE305, Spring 2010 5 Biot-Savart Law (Integral form) Biot-Savart Law (Integral form) 2 1) 2) 0 3) 0 4) 4 v s r t d Id a r ρ π ∇• = - ∇• = = × = J J J S L H Ñ Ñ 1) Continuity equation 2) Restricting our discussion to DC currents only 3) From the divergence theorem. The total current crossing any closed surface is zero Condition may be satisfied only by assuming a currrent flowing around a closed path It is this current flowing in a closed surface which must be our experimental source, not the differential element 4) Biot-Savart Law (Integral Form)

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