lecture9 - 1 ECE 303 Fall 2007 Farhan Rana Cornell...

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Unformatted text preview: 1 ECE 303 Fall 2007 Farhan Rana Cornell University Lecture 9 Magnetoquasistatics In this lecture you will learn: Basic Equations of Magnetoquasistatics The Vector Potential The Vector Poissons Equation The Biot-Savart Law Magnetic Field of Some Simple Current Carrying Elements The Magnetic Current Dipole ECE 303 Fall 2007 Farhan Rana Cornell University Equations of Magnetoquasistatics ( ) t r E o , . r r = = E r . = H o r ( ) t r J H , r r r = Equations of Electroquasistatics Equations of Magnetoquasistatics Electric fields are produced by only electric charges Once the electric field is determined, the magnetic field can be found by the last equation above Magnetic fields are produced by only electric currents Once the magnetic field is determined, the electric field can be found by the last equation above Currents in magnetoquasistatics are solenoidal (i.e. with zero divergence) t E J H o + = r r r t H E o = r r In magnetoquasistatics the source of the magnetic field is electrical current ( ) ( ) . , . = = H t r J r r r 2 ECE 303 Fall 2007 Farhan Rana Cornell University Amperes Law for Magnetoquasistatics = a d J s d H r r r r . . A closed contour Amperes Law : The line integral of magnetic field over a closed contour is equal to the total current flowing through that contour Right Hand Rule: The positive directions for the surface normal vector and of the contour are related by the right hand rule electric current density J H r r = ECE 303 Fall 2007 Farhan Rana Cornell University 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 Use amperes law on the closed contour shown by the dashed line: ( ) ( ) ( ) r I r H I r H r a d J s d H 2 2 . . = = = r r r r r Magnetic field is entirely in the direction and falls off as ~1/ r from the line-current Working in the cylindrical coordinates s d r 3 ECE 303 Fall 2007 Farhan Rana Cornell University Magnetic Field of a Solenoid Consider a solenoid with N turns per unit length and carrying a current I The magnetic field inside the solenoid is uniform and strong There is a fringing field outside the solenoid which is very weak and may be neglected Assumptions: I H L ( ) NI H I LN H L a d J s d H y y = = = r r r r . ....
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lecture9 - 1 ECE 303 Fall 2007 Farhan Rana Cornell...

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