PHY2049ch29A%282-24-10%29

PHY2049ch29A%282-24-10%29 - Chapter 29 Creating Magnetic...

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Unformatted text preview: Chapter 29: Creating Magnetic Fields PHY2049: Chapter 29 1 Creating Magnetic Fields Sources of magnetic fields Spin of elementary particles (mostly electrons) Atomic orbits (L > 0 only) Moving charges (electric current) Currents generate the most intense magnetic fields Discovered by Oersted in 1819 (deflection of compass needle) Four examples studied here Long wire Wire loop Partial wire loops Solenoid PHY2049: Chapter 29 2 B Field Around Very Long Wire Field around wire is circular, intensity falls with distance Direction given by RHR (compass follows field lines) Right Hand Rule #2 PHY2049: Chapter 29 3 B Field Around Wire PHY2049: Chapter 29 4 Long Wire B Field Example I = 500 A toward observer. Find B vs r RHR field is counterclockwise μ0 i B= = 2r r r r r r r r = = = = = = = ( 4 10 7 2r B B B B B B B = = = = = = = )500 = 10 = = = = = = = 4 r 0.001 m 0.005 m 0.01 m 0.05 m 0.10 m 0.50 m 1.0 m 0.10 T 0.02 T 0.010 T 0.002 T 0.001 T 0.0002 T 0.0001 T 1000 G 200 G 100 G 20 G 10 G 2G 1G PHY2049: Chapter 29 5 Charged Particle Moving Near Wire Wire carries current of 400 A upwards Proton moving at v = 5 106 m/s downwards, 4 mm from wire Find magnitude and direction of force on proton Solution Direction of force is to left, away from wire Magnitude of force at r = 4 mm F = 1.6 10 ( 19 )( 5 106 ) 2 10 7 400 0.004 v I PHY2049: Chapter 29 6 Derivation of B Field Around Long Wire Biot-Savart law μ0 i ds sin dB = 4 r2 Integrate over path Line, ring, etc Direction of B field ˆ μ0 i ds r dB = 4 r2 This is most general way to calculate any magnetic field PHY2049: Chapter 29 7 Long Wire Calculation Integrate along wire: <s< μ0 i ds sin dB = 4 r2 r= s +R 2 2 sin = R s 2 + R2 B= μ0 iR ds 4 s 2 + R2 ( ) 3/2 μ0i s = 4 R s 2 + R2 μ0i = 2R PHY2049: Chapter 29 8 B Field at Center of Circular Current Loop Integrate around loop: 0 r = R = constant ds = Rd sin = 1 B field points up out of page R 2 r ds x All contributions on loop are identical B= 2 0 μ0 i ds = 2 4r 2 0 μ0 i Rd μ0i = 2 4R 2R μ0i B= 2R PHY2049: Chapter 29 9 Circular Current Loop (cont) Field at any point inside circle can be calculated also Biot-Savart shows that field is upward inside loop RHR #3 (see picture) If N turns close together in loop Field multiplied by N At center PHY2049: Chapter 29 10 N Turn Current Loop Example i = 500 A, r = 5 cm, N = 20. Find B at center of coil. μ0 i B= N = 2r ( )( 20 4 10 7 2 0.05 )(500) = 1.26 T PHY2049: Chapter 29 11 Force Between Two Parallel Currents Force on I2 from I1 RHR Force towards I1 Force on I1 from I2 μ0 I 2 μ0 I1 I 2 F1 = I1 B2 L = I1 L L= 2r 2r RHR Force towards I2 I2 I1 Magnetic forces attract two parallel currents I2 I1 PHY2049: Chapter 29 12 Force Between Two Anti-Parallel Currents Force on I2 from I1 RHR Force away from I1 Force on I1 from I2 RHR Force away from I2 I2 I1 Magnetic forces repel two antiparallel currents I2 I1 PHY2049: Chapter 29 13 Parallel Currents (cont.) Look at them edge on to see B fields more clearly B B 2 1 F Antiparallel: repel 2 F 1 B 2 F 1 Parallel: attract 2 F 1 B PHY2049: Chapter 29 14 Ampere’s Law Take arbitrary path around set of currents Let ienc be total enclosed current (+ up, down) Let B be magnetic field, and ds be differential length along path Not included in ienc 1 Only currents inside path contribute! 5 currents inside path (included) 1 outside path (not included) 3 2 4 5 6 B d s = μ0 ( i2 + i3 + i4 i5 i6 ) Similar to Gauss’ law, except around closed path PHY2049: Chapter 29 15 Sign of Contribution B d s = μ0 ( i1 i2 ) PHY2049: Chapter 29 16 ...
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This note was uploaded on 05/17/2011 for the course PHY 2049 taught by Professor Any during the Spring '08 term at University of Florida.

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