lec27_032107_-_Faradays_Law_II

lec27_032107_-_Faradays_Law_II - Faraday's Law II Faraday'...

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Unformatted text preview: Faraday's Law II Faraday' emf = Ed = - d dt ( B dA) = - ddt Direction B 1. Direction of Curly E-field: EPoint your thumb in the direction opposite of the time-varying B-field, dB timeB-field, - dt then your fingers curl in the direction of the curly E-field E NC . E- We are going to take it apart, and then put it back together again so that it will be meaningful! Wednesday, 21 March 2007 1 Wednesday, 21 March 2007 2 Direction 1. Direction of Curly E-field: EE NC B2 t2 P Question dB dt need B t dB dt want - dB dt - t1 B1 estimate with E NC B = Bf - Bi t2 P t1 = B2 - B1 - B1 = B2 + - B1 ( ) B2 dB dt - dB dt B1 At the origin, what is the direction of B ? A. +x E. Zero magnitude B. -x C. +y D. -y B Wednesday, 21 March 2007 3 Wednesday, 21 March 2007 4 1 Question The magnet is moving in the +z direction, away from the coil. At the origin (inside the coil), what is the direction of dB ? Question - dt The magnet is moving in the +z direction, away from the coil. At a location A on the y-axis (inside the coil), what is ythe direction of E NC ? A. +x B. -x C. +y D. -y E. Zero magnitude A. +x B. -x C. +z D. -z Wednesday, 21 March 2007 E. Zero magnitude 5 Wednesday, 21 March 2007 6 Magnitude 2. Magnitude of Curly E-field: ERate of change of the magnetic flux through a surface area! at t : magnetic field as shown B = 0.5 T i Question B i = B dA BA = 510-5 T m2 at t f : magnetic field is zero B f = 0 0.01 m A long solenoid of radius 2 cm has a B-field of 0.5 T Binside. What is the magnetic flux through the outer ring of radius 10 cm? cm? A A. 0 Tm2 B. 2 e-4 Tm2 C. 2 e-2 Tm2 D. 0.5 e-2 Tm2 0.5 7 Wednesday, 21 March 2007 I 0.01 m Wednesday, 21 March 2007 dB B B f - Bi = dt t f - ti t . e-1 Tm2 8 2 Question Magnetic flux inside the solenoid changes from 5 Tm2 to 3 Tm2 in 0.1 s. s. What is the emf in the outer ring? d Ed = - dt ( B dA) Faraday's Law Faraday' emf = - Relates a time-varying B-field at some location in timeBspace to a curly E-field around that area. E- d B dt A. 0 V B. 0.2 V C. 2 V D. 20 V Wednesday, 21 March 2007 dB Fingers curl in E NC dt Quantitatively, we related integral of the curly E-field around Ea closed path to the rate of change of the magnetic flux on a surface enclosed by that path. path. Direction: Thumb points in - emf = E d N turns in the coil: 9 Wednesday, 21 March 2007 B = B dA E d = -N d dt ( B dA) E. 80 V emf = - N d B dt 10 B Example What is the induced emf in the ring? B Example What is the induced emf in the coil? = d B dt = BA sin (t ) R B = B dA = B A = BA cos = BA cos(t ) R If the ring has a resistance of 2 , what is the induced current? current? = IR I= = d Ed = - dt ( B dA) = d [BA cos(t )] dt = - BA sin (t ) = BA sin (t ) 11 d Ed = - B dA dt BA sin (t ) R R ( ) Wednesday, 21 March 2007 Wednesday, 21 March 2007 12 3 d = Ed = - dt Lenz's Law Lenz' ( d B B dA = - dt ) Question What will be the direction of the current through R2 immediately after the switch is closed? Change is Bad! A. Left B. Right C. Zero D. Cannot be determined Wednesday, 21 March 2007 13 Wednesday, 21 March 2007 14 The bar shown is given an initial velocity V, and slides on frictionless rails. Describe its subsequent motion: Question Motional emf Lenz's Law Faraday's Law Lenz' Faraday' d B = Binduced dt B = B dA = B dA = B dA A. It continues to move with constant velocity V; B. It accelerates to the right constantly increasing speed; C. It accelerates to the right until it reaches a constant maximum speed; D. It accelerates to the left until it stops, then reverses direction and moves to the left; E. It experiences simple harmonic motion. Wednesday, 21 March 2007 15 d B d = (B x ) dt dt dx =B dt =B v = d B =B v dt = BA =B x Wednesday, 21 March 2007 I= R = B v R 16 4 B A Single Bar qv B E v Eddy Currents & Magnetic Breaks FB = FE qvB = qE vB = E F =0 emf I B Induced emf! emf! Induced I! qE = Ed = E d =E d =E Wednesday, 21 March 2007 E= vB = Induced emf in an airplane: B = 0.0005 T v = 340 m/s (Mach 1) = 10 m F =0 F Lenz's law: This current must experience a magnetic force Lenz' that opposes the rotation of the disk = vB = 1.7 V! 17 F = I B I must point down Wednesday, 21 March 2007 Interaction between Eddy Current & B-field causes a braking action on the disk! 18 Eddy Currents & Magnetic Breaks v1 v2 v3 S N N S Eddy Currents & Magnetic Breaks induced I induced emf induced emf induced Binduced emf induced I induced emf induced Binduced I induced emf induced B Binduced I induced B S N S N induced I induced F = I B Wednesday, 21 March 2007 F = I B F = I B 19 Wednesday, 21 March 2007 20 5 ...
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