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Lecture 6 Magnetic Fields Elect romoti ve F orce (EMF) Magg()netomotive Force (MMF) ’s Equations in Integral Form

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Magnetic Force Field

• Just as the E was defined to “explain” (patch over) the force acting between two stationary charges, the B was defined to “explain” the force acting between two current- carrying loops of wire: • F =Q= QV X B • dF = IdL X B

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9/15/2009 ECE342 EMC (KEH) 4 Therefore the force on a current-carrying wire segment

I1dl1 in the presence of the density dB produced by a current -carrying wire segment Id l is given

by: dF = I1dl1 x dB

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9/15/2009 ECE342 EMC (KEH) 6 B = Bx(y) ix

∞

ix

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9/15/2009 ECE342 EMC (KEH) 10 = Weber/meter2 (Web er = vo lt-)

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9/15/2009 ECE342 EMC (KEH) 34 x

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9/15/2009 ECE342 EMC (KEH) 42 H = HΦiΦ =[I/(2[ I/ (2 π r)] iΦ

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9/15/2009 ECE342 EMC (KEH) 56 In summary (From Wikipedia!)

Name Differential form Integral form 's law:

Gauss' law for (absence of magnetic monopoles):

Faraday's law of induction:

Ampère's law (with Maxwell's extension):

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