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Unformatted text preview: Engineering ElectroMagnetics Engineering ElectroMagnetics ECE305, 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 CrossSectional Example CrossSectional 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.
 Spring '08
 Staff
 Electromagnet

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