Lectures_Lect14

# Lectures_Lect14 - Phys ic s 212 Le c ture 14 S lide Phys ic...

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Unformatted text preview: Phys ic s 212 Le c ture 14, S lide Phys ic s 212 Le c ture 14, S lide 1 Physics 212 Physics 212 Lecture 14 Lecture 14 Biot-Savart Law Biot-Savart Law 2 ˆ 4 I ds r dB r μ π × = :05 Phys ic s 212 Le c ture 14, S lide Phys ic s 212 Le c ture 14, S lide 2 Biot-Savart Law: Biot-Savart Law: :05 2 ˆ 4 I ds r dB r μ π × = We can use this law to calculate the magnetic field produced by We can use this law to calculate the magnetic field produced by ANY ANY current current distribution distribution BUT BUT Easy analytic calculations are possible only for a few distributions: Easy analytic calculations are possible only for a few distributions: Infinite Straight Wire Infinite Straight Wire Axis of Current Loop Axis of Current Loop Field at the center of a ring P ds r ds ˆ r d B P d B points out of page for each ds I 2 2 4 4 P P I I d s r d d B d B r r μ μ θ π π = = = 2 2 4 2 P I I B d B d r r π π μ μ θ π = = = ds r d θ = d θ 2 ˆ ˆ 4 I ds xr r d B r r r μ π = = Physics 212 Lecture 14, Slide Physics 212 Lecture 14, Slide 4 B fro m infinite line o f c urre nt Current I OUT • r = dis ta nc e fro m wire 7 4 10 / Tm A μ π- = 2 I B r μ π = r Ma g nitude : B :07 Dire c tio n: Thumb: on I Fingers: curl in direction of B Current in Wire Current in Wire Resulting B f ield Resulting B f ield I I Physics 212 Lecture 14, Slide Physics 212 Lecture 14, Slide 5 A long straight wire is carrying current from left to right. Two identical charges are moving with equal speed. Compare the magnitude of the force on charge a moving directly to the right, to the magnitude of the force on charge b moving up and to the right at the instant shown (i.e. same distance from the wire). a) |F a |> |F b | b) |F a |= |F b | c) |F a |< |F b | v I v (a) r r (b) 28 Currents + Charges F qv B = | | sin F qvB θ = Same q, |v|, B and θ (=90) :10 • B Forces are in different directions • F F Physics 212 Lecture 14, Slide Physics 212 Lecture 14, Slide 6 Two long wires carry equal and opposite currents What is the direction of the magnetic field above, and midway between the two wires carrying current – at the point marked “X”? x Magnetic Fields obey superposition A) Left B) Right C) Up D) Down E) Zero B x :13 Physics 212 Lecture 14, Slide Physics 212 Lecture 14, Slide 7 Force between current-carrying wires • I 1 F Conclusion: Currents in same direction attract....
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Lectures_Lect14 - Phys ic s 212 Le c ture 14 S lide Phys ic...

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