lecture20 - Sources of Magnetic Fields Sources

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Sources of Magnetic Fields Sources of Magnetic Fields
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    Besides magnetic poles,  electric currents create  magnetic  fields. There are two ways of calculating  B produced by currents: i) Biot-Savart Law : Field of a “current element” (analogous to a point charge in electrostatics). ii) Ampère’s Law :  An integral theorem similar to        Gauss’s law.
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m/A T 10 4 7 o × = - π μ ˆ 4 2 o r I r ds dB × = We get the total  B by integrating ds along the wire : (“permeability of vacuum”) I I θ ds r r dB ˆ 4 2 o × = r I r ds B Biot-Savart Law Biot-Savart Law
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Question: When is d B =0 ? How does d B  vary with r ?  Current I in a straight wire  What is the direction of  B  at points a and b ?  a b
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Example 1 Example 1 Find  B  at a distance R from a long straight wire x y I R φ dx dB θ i ds ˆ = dx direction) - z   (in     o dx r I dB 2 sin 4 θ π μ = (note  sin   = R/r = cos  θ ) r
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lecture20 - Sources of Magnetic Fields Sources

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