Notes on Chapter 29 - - Chapter 29 Magnetic Fields Due to...

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1 July 2010 1 - Chapter 29 – Magnetic Fields Due to Currents 29-1 What is Physics? A moving charged particle (i.e., a current) produces a magnetic field. In this chapter we determine the magnetic field due to current in a very small section of current-carrying wire. We then extend the method to calculate the magnetic fields due to different wire configurations
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1 July 2010 2 76 0 4 x10 . / 1.26x10 . / Tm A µπ −− = Permeability constant is defined numerically as: Consider the magnetic field due to the current in a small section ds of current carrying wire. We take the direction of the length vector to be the same as the current direction ds µ θ π = 0 2 sin 4 The magnitude of the field due to the current-length element at is found to be ds P : i i ds r dB 29-2 Calculating the Magnetic Field Due to a Current
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1 July 2010 3 Use right-hand rule to find the direction of as the direction of dB x ds r  00 23 ˆ xx 44 ids r ids r dB rr µµ ππ = =   Biot-Savart Law ˆ Used: r r r = Experimental inverse-square law
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1 July 2010 4 Magnetic Field Due to a Current in a Long (infinite) Straight Wire 0 2 i B x µ π =
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1 July 2010 5 0 2 sin 4 µ φ π = idl r dB d l dy = 22 r xy = sin sin ( ) xx r πφ = + = −= 0 2 2 3/2 00 222 4 4 () 2 4 a a a a i y ix i xxy xdy B dB a a   +  = = ∫∫ + = = + i Used Integral 19 on page A -11
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1 July 2010 6 22
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Notes on Chapter 29 - - Chapter 29 Magnetic Fields Due to...

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