Lect08MagStatic - ECE 3030 Electromagnetic Fields and Waves...

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1 ECE 3030 Electromagnetic Fields and Waves Fall 2009 Lecture 8 2009/9/14 Magnetoquasistatics Basic Equations Vector Potentia 1 Swartz and Rana 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 8: Instructor: Dr. Wesley E. Swartz Vector Potential Magnetic Fields From Selected Current Structures I H I ' s d ' r r x y z r ' r n ˆ Problem Assignments Demo 3 (Tuesday, September 15) : Problem 4.3 – Multiple charge images Problem 4.14 – Poisson’s Equation Problem 5.6 – Charge above dielectric, looks difficult, tricky, but short Checking solution 4.14 to Poisson’s Equation Workshop 3 (Thursday, September 17) : Finish checking solution 4.14 Problem 4.5 – Spherical symmetry Problem 4 13 Sphere immersed in uniform field 2 Swartz and Rana 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 8: Problem 4.13 – Sphere immersed in uniform field Start Homework 3 as time permits Homework 3 (due Tuesday, September 22 by 1pm) : Problem 4.15 – Loop of charge next to a conductor Problem 5.7 – Loop of charge next to a dielectric Equations of Magnetoquasistatics In magnetostatics or magnetoquasistatics the source of the magnetic field is an electrical current. 0 = H o μ () t r J H , = × Equations of Electroquasistatics Equations of Magnetoquasistatics t r E o , ρ ε = 0 = × E 3 Swartz and Rana 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 8: t H E o = × t E J H o + = × Magnetic fields are produced only by electric currents. Once the magnetic field is determined, the electric field can be found with the last equation. Electric fields are produced only by electric charges. Once the electric field is determined, the magnetic field can be found with the last equation. Ampere’s Law for Magnetoquasistatics Ampere’s Law: The line integral of magnetic field along a closed contour is equal to the total current flowing through that contour.  = a d J s d H J H = × Surface normal 4 Swartz and Rana 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 8: A closed contour Right Hand Rule: The positive directions for the surface normal vector and of the contour direction are related by the right hand rule. Electric current density Use Ampere’s Law on the closed contour shown by the dashed line: Magnetic Field of an Infinite Line-Current Consider an infinitely long line-current carrying a total current I in the + z -direction, as shown below. x y line current ( ) ( ) I r H r a d J s d H π φ 2 = =  s d 5 Swartz and Rana 06/5/25 Electromagnetic Fields and Waves – Fall 2009 Lecture 8: The magnetic field is entirely in the direction and falls off as 1/r from the line current.
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This note was uploaded on 11/26/2009 for the course ECE 3030 at Cornell University (Engineering School).

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Lect08MagStatic - ECE 3030 Electromagnetic Fields and Waves...

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