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Lecture21 - Physics 132 Introductory Physics Electricity...

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1 February 25, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 1 Physics 132 Introductory Physics: Electricity and Magnetism Winter Quarter 2008 Lecture 21 February 25, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 2 Electric Currents and Magnetic Fields Electric currents feel forces due to magnetic fields. They also create magnetic fields! Field lines encircle the currents which are their source. Right hand rule: Thumb along i, fingers curl in direction of B
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2 February 25, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 3 Biot-Savart Law dB = μ 0 4 π id s × r r 3 Integration of the Biot-Savart* law gives B field for a current distribution: * (They’re French, so the final t’s are silent.) This is an inverse-square law, just like Coulomb’s law. μ 0 is the permeability constant. μ 0 4 π × 10 7 Tm A February 25, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 4 Magnetic Field of a Long Straight Wire d B = μ 0 4 π id s × r r 3 = μ 0 i 4 π sin( θ ) ds r 2 y x z y r 2 = R 2 + s 2 sin( θ ) = sin( π θ ) = R R 2 + s 2 B = μ 0 i 4 π y R R 2 + s 2 ( ) 3 2 ds = −∞ + μ 0 i 2 π y R R 2 + s 2 ( ) 3 2 ds 0 + = μ 0 i 2 π y 1 R 2 + s 2 ( ) 1 2 s = 0 s = = μ 0 i 2 π R y B falls as 1/R for an infinite wire.
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3 February 25, 2008 Physics 132-Winter 2008 Prof. Jim Beatty-Ohio State 5 Living Near Power Lines Power lines carry electric power across long distances at high voltages (50-500 kV) and currents of ~500A.
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