ECE-305-Lecture15

ECE-305-Lecture15 - Engineering Electro-Magnetics...

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Unformatted text preview: Engineering Electro-Magnetics Engineering Electro-Magnetics ECE-305, Lecture 15 Dennis McCaughey, Ph.D. 18 March 2010 03/18/2010 Dennis McCaughey, ECE305, Spring 2010 2 Ampere’s Law Ampere’s Law The line integral of the tangential component of the magnetic field strength around a closed path is equal to the current enclosed by that path. Current is usually known and the law provides a method of determining H Similar to Gauss’ Law in that a good deal of symmetry is required to calculate – At each point of the closed path H is either tangential or normal to the path – H has the same value at all points of the path where H is tangential ∫ = • enc I dL H 03/18/2010 Dennis McCaughey, ECE305, Spring 2010 3 Closed Paths Closed Paths A conductor has a total current I. The line integral of H about the closed paths a and b is equal to I . The integral around path c is less than I since the entire current is not enclosed by that path. 03/18/2010 Dennis McCaughey, ECE305, Spring 2010 4 Coaxial Cable Coaxial Cable ( a) Cross section of a coaxial cable carrying a uniformly distributed current I in the inner conductor and -I in the outer conductor. – The magnetic field at any point is most easily determined by applying Ampere’s circuital law about a circular path (b) Current filaments produce the magnetic field shown 03/18/2010 Dennis McCaughey, ECE305, Spring 2010 5 Continuing Continuing ( 29 ( 29 ( 29 2 1 1 2 2 2 2 2 Symmetry: is not a function of or z Components at = and = cancel Therefore only a component 2 2 2 encl H d H d I I I I H a a H I a b a H I a a π φ φ φ φ φ ρ ρ ρ φ φ φ ρ φ πρ π ρ πρ πρ ρ ρ ρ π = < ± • = = < < < = < < = = ∫ ∫ H L Ñ ( 29 ( 29 2 2 2 2 2 2 2 2 If the radius is larger than the outer conductor no current is enclosed If the path lies within the outer conductor 2 2 H b c b H I I c b I c H b c c b φ φ ρ ρ ρ πρ ρ ρ πρ = < < - =- - - = < < - 03/18/2010 Dennis McCaughey, ECE305, Spring 2010 6 Cross-Sectional Example Cross-Sectional Example The magnetic field intensity is continuous There are no sudden jumps The external field is zero This is an example of “shielding” The magnetic field intensity as a function of radius in an infinitely long coaxial transmission line with the dimensions shown 03/18/2010 Dennis McCaughey, ECE305, Spring 2010 7 Solenoid Solenoid 03/18/2010 Dennis McCaughey, ECE305, Spring 2010...
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This note was uploaded on 09/13/2011 for the course ECE 305 taught by Professor Staff during the Spring '08 term at George Mason.

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ECE-305-Lecture15 - Engineering Electro-Magnetics...

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