Lect17 - Physics 212 Lecture 17 Faraday’s Law rr dΦ B...

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Unformatted text preview: Physics 212 Lecture 17 Faraday’s Law rr dΦ B emf = ∫ E ⋅ d l = − dt Physics 212 Lecture 17, Slide 1 Music Who is the Artist? BB A) B) C) D) E) Albert Collins Buddy Guy B. B. King John Lee Hooker Robert Cray Great Album Duets with: 1. All of the choices 2. Etta James, 2. Irma Thomas, Koko Taylor, Koko Katie Webster, Ruth Brown…. Why? I keep saying BB every lecture.. Should play BB King ! Distinctive guitar and voice… Physics 212 Lecture 17, Slide 2 Your Comments “How to determine the direction of the induced How current resulting from an EMF, much like these preflight questions.” preflight “Lenz' Law and why it is so.” Lenz’ law (direction of induced emf) law emf can be understood in terms of conservation of energy “I would really still like to understand these would generator examples. Also, I'm still not sure about what the minus sign means in Faraday's Law.” what “Isn't this the material that was covered on the Isn't homework do this week? Or are we just learning the same thing again but giving it different names. Also, ....are we going to have the review thing online that we did last time. I found it extermely extermely helpful while studying for the first exam.” “this was a good preflight. AND CAN YOU this PLEASE TELL PEOPLE SITTING IN THE BACK TO SHUT UP!!!!!!!!!!!! PHYSICS CLASSES ARE ANNOYING NOW.” ARE 05 I’m getting a lot of these Please show some consideration !! We will discuss the relation We between motional emf and emf and Faraday’s law Faraday 40 30 20 10 0 Confused Confident Physics 212 Lecture 17, Slide 3 Plan • Introduce Faraday’s Law • Show how Faraday’s Law explains motional emf examples • Stress genesis of new theory – Faraday’s Law predicts (correctly) induced emf for cases where there is no motional emf ! Physics 212 Lecture 17, Slide 4 Faraday’s Law: rr dΦ B emf = ∫ E ⋅ d l = − dt where rr Φ B ≡ ∫ B ⋅ dA Looks scary but it’s not – its amazing and beautiful ! not its A changing magnetic flux produces an electric field. Electricity and magnetism are deeply connected Physics 212 Lecture 17, Slide 5 Faraday’s Law: rr dΦ B emf = ∫ E ⋅ d l = − dt where rr Φ B ≡ ∫ B ⋅ dA In Practical Words: 1) When the flux ΦB through a loop changes, an emf is induced in the through emf is loop. loop. B Flux A Show Projection Think of ΦB as the number of field lines passing through the surface There are many ways to change this… Physics 212 Lecture 17, Slide 6 Faraday’s Law: rr dΦ B emf = ∫ E ⋅ d l = − dt where rr Φ B ≡ ∫ B ⋅ dA In Practical Words: 1) When the flux ΦB through a loop changes, an emf is induced in the through emf is loop. loop. B Change the B field A Physics 212 Lecture 17, Slide 7 Faraday’s Law: rr dΦ B emf = ∫ E ⋅ d l = − dt where rr Φ B ≡ ∫ B ⋅ dA In Practical Words: 1) When the flux ΦB through a loop changes, an emf is induced in the through emf is loop. B Move loop to a place where the B field is different the A Physics 212 Lecture 17, Slide 8 Faraday’s Law: rr dΦ B emf = ∫ E ⋅ d l = − dt where rr Φ B ≡ ∫ B ⋅ dA In Practical Words: 1) When the flux ΦB through a loop changes, an emf is induced in the through emf is loop. B Rotate the loop Rotate A Physics 212 Lecture 17, Slide 9 Faraday’s Law: rr dΦ B emf = ∫ E ⋅ d l = − dt where rr Φ B ≡ ∫ B ⋅ dA In Practical Words: 1) When the flux ΦB through a loop changes, an emf is induced in the through emf is loop. B Rotate the loop Rotate A Physics 212 Lecture 17, Slide 10 10 Faraday’s Law: rr dΦ B emf = ∫ E ⋅ d l = − dt where rr Φ B ≡ ∫ B ⋅ dA In Practical Words: 1) When the flux ΦB through a loop changes, an emf is induced in the through emf is loop. B Rotate the loop Rotate A Physics 212 Lecture 17, Slide 11 11 Faraday’s Law: rr dΦ B emf = ∫ E ⋅ d l = − dt where rr Φ B ≡ ∫ B ⋅ dA In Practical Words: 1) When the flux ΦB through a loop changes, an emf is induced in the through emf is loop. loop. 2) The emf will make a current flow if it can (like a battery). 2) emf I Demo Coil and magnet Physics 212 Lecture 17, Slide 12 12 Faraday’s Law: rr dΦ B emf = ∫ E ⋅ d l = − dt where rr Φ B ≡ ∫ B ⋅ dA In Practical Words: 1) When the flux ΦB through a loop changes, an emf is induced in the loop. through emf is 2) The emf will make a current flow if it can (like a battery). emf 3) The current that flows induces a new magnetic field. I Physics 212 Lecture 17, Slide 13 13 Faraday’s Law: rr dΦ B emf = ∫ E ⋅ d l = − dt where rr Φ B ≡ ∫ B ⋅ dA In Practical Words: 1) When the flux ΦB through a loop changes, an emf is induced in the loop. through emf is 2) The emf will make a current flow if it can (like a battery). emf 3) The current that flows induces a new magnetic field. 4) The new magnetic field opposes the change in the original magnetic field netic that created it. (Lenz’ Law) that B dB/dt Physics 212 Lecture 17, Slide 14 14 Faraday’s Law: rr dΦ B emf = ∫ E ⋅ d l = − dt where rr Φ B ≡ ∫ B ⋅ dA In Practical Words: 1) When the flux ΦB through a loop changes, an emf is induced in the loop. through emf is 2) The emf will make a current flow if it can (like a battery). emf 3) The current that flows induces a new magnetic field. 4) The new magnetic field opposes the change in the original magnetic netic field. (Lenz’ Law) field. B Demo dB/dt Physics 212 Lecture 17, Slide 15 15 Faraday’s Law: rr dΦ B emf = ∫ E ⋅ d l = − dt where rr Φ B ≡ ∫ B ⋅ dA Executive Summary: emf→current→field a) induced only when flux is changing a) only when flux b) opposes the change b) opposes Physics 212 Lecture 17, Slide 16 16 BB Preflight 2 • Motional emf is ZERO Motional emf •vXB=0 50 • no charge separation • no E field 40 • no emf no emf 30 • The flux is NOT changing 20 • B does not change 10 • the area does not change • the orientation of B and A does not change 0 Physics 212 Lecture 17, Slide 17 17 BB Looking from right XXXXXXXX XXXXXXXX Preflight 4 XXXXXXXX XXXXXXXX XXXXXXXX • Motional emf is ZERO Motional emf • There is no motion of conduction electrons ! Clockwise restores B 60 • HOWEVER: The flux IS changing 50 • B decreases in time • current induced to oppose the flux change 40 • clockwise current puts back B that was 30 clockwise removed removed 20 THIS IS NEW !! Faraday’s Law explains existence of emf Law emf when the motional emf is ZERO! when emf 10 0 Physics 212 Lecture 17, Slide 18 18 BB Preflight 6 Current changes direction every time the loop Current becomes perpendicular with the B field becomes emf ~ dΦ/dt 60 50 40 30 (B ∏ dA = max) fl d/dt (B ∏ dA ) = 0 (B max) O X B dA O B X 20 10 dA 0 Physics 212 Lecture 17, Slide 19 19 F O X BB B B Like poles repel Like Preflight 8 Ftotal < mg a<g (copper is not ferromagnetic) 50 This one is hard ! B field increases upward as loop falls Clockwise current (viewed from top) is induced Clockwise 40 30 20 10 0 Physics 212 Lecture 17, Slide 20 20 HOW HOW IT WORKS WORKS Looking down B Preflight 8 B I I IL X B points UP (copper is not ferromagnetic) This one is hard ! B field increases upward as loop falls Clockwise current (viewed from top) is induced Clockwise Main Field produces horizontal forces Main Fringe Field produces vertical force Ftotal < mg a<g Demo ! dropping magnets e-m cannon Physics 212 Lecture 17, Slide 21 21 Calculation A rectangular loop (height = a, length = b, resistance = R, mass = m) coasts with a constant velocity v0 in + x direction as shown. At t =0, the loop enters a region of constant magnetic field B directed in the –z direction. y a v0 B bxxxxxxx xxxxxxx xxxxxxx xxxxxxx x What is the direction and the magnitude of the force on the loop when half of it is in the field? • Conceptual Analysis – – Once loop enters B field region, flux will be changing in time Faraday’s Law then says emf will be induced • Strategic Analysis – – – Find the emf Find the current in the loop Find the force on the current Physics 212 Lecture 17, Slide 22 22 emf = − Calculation A rectangular loop (height = a, length = b, resistance = R, mass = m) coasts with a constant velocity v0 in + x direction as shown. At t =0, the loop enters a region of constant magnetic field B directed in the –z direction. dΦ B dt y BB a v0 B bxxxxxxx xxxxxxx xxxxxxx xxxxxxx x What is the magnitude of the emf induced in the loop just after it enters the field? (A) ε = Babv02 (A) (B) ε = ½ Bav0 (C) ε = ½ Bbv0 (D) ε = Bav0 (E) ε = Bbv0 (B) (C) (D) (E) y a v0 B xxxxxxx b xxxxxxx a xxxxxxx xxxxxxx Change in Flux = dΦB = BdA = Bav0dt Change BdA x In a time dt In dt it moves by v0dt it The area in field The changes by dA = v0dt a dA dt dΦ B = Bavo dt Physics 212 Lecture 17, Slide 23 23 Calculation Calculation A rectangular loop (height = a, length = b, resistance = R, mass = m) coasts with a constant velocity v0 in + x direction as shown. At t =0, the loop enters a region of constant magnetic field B directed in the –z direction. emf = − y a BB v0 dΦ B dt B bxxxxxxx xxxxxxx xxxxxxx xxxxxxx x What is the direction of the current induced in the loop just after it enters the field? (A) clockwise (A) (B) counterclockwise (B) (C) no current is induced (C) emf is induced in direction to oppose the change in flux that produced it y a v0 B bxxxxxxx xxxxxxx xxxxxxx xxxxxxx Flux is increasing into the screen Induced emf produces flux out of screen Induced emf produces x Physics 212 Lecture 17, Slide 24 24 Calculation emf = − y A rectangular loop (height = a, length = b, resistance = R, mass = m) coasts with a constant velocity v0 in + x direction as shown. At t =0, the loop enters a region of constant magnetic field B directed in the –z direction. BB a v0 dΦ B dt B bxxxxxxx xxxxxxx xxxxxxx xxxxxxx x What is the direction of the net force on the loop just after it enters the field? (A) +y (A) (B) -y (B) (C) +x (C) (D) -x Force on a current in a magnetic field: r rr F = IL × B y b a B xxxxxxx v0 I xxxxxxx • Force on top and bottom segments cancel (red arrows) • Force on right segment is directed in –x direction. Force x Physics 212 Lecture 17, Slide 25 25 Calculation A rectangular loop (height = a, length = b, resistance = R, mass = m) coasts with a constant velocity v0 in + x direction as shown. At t =0, the loop enters a region of constant magnetic field B directed in the –z direction. What is the magnitude of the net force on the loop just after it enters the field? (A) F = 4aBvo R (B) F = a 2 Bvo R (A) 2 (C) F = a 2 B 2vo / R r rr F = IL × B emf = − y a BB v0 dΦ B dt B bxxxxxxx xxxxxxx xxxxxxx xxxxxxx x r rr F = IL × B ε = Bav0 (D) F = a 2 B 2vo / R rr F = ILB since L ⊥ B y b a F B xxxxxxx v0 I ε Bavo I= = R R xxxxxxx B 2 a 2vo Bavo F = aB = R R ILB x Physics 212 Lecture 17, Slide 26 26 Follow-Up A rectangular loop (sides = a,b, resistance = R, mass = m) coasts with a constant velocity v0 in + x direction as shown. At t =0, the loop enters a region of constant magnetic field B directed in a the –z direction. t = dt: ε = Bav0 y b v0 B xxxxxxx xxxxxxx xxxxxxx xxxxxxx BB x What is the velocity of the loop when half of it is in the field? Which of these plots best represents the velocity as a function of time as the loop moves form entering the field to halfway through ? (A) (B) (C) D) (E) (A) X This is not obvious, but we know v must decrease Why? X b a Fright B xxxxxxx v0 I xxxxxxx X Fright points to left Acceleration negative Speed must decrease Physics 212 Lecture 17, Slide 27 27 Follow-Up A rectangular loop (sides = a,b, resistance = R, mass = m) coasts with a constant velocity v0 in + x direction as shown. At t =0, the loop enters a region of constant magnetic field B directed in the –z direction. y b a What is the velocity of the loop when half of it is in the field? v0 B xxxxxxx xxxxxxx xxxxxxx xxxxxxx ε = Bav0 x Which of these plots best represents the velocity as a function of time as the loop moves form entering the field to halfway through ? dv (A) (D) F = a B v/ R = m • Why (D), not (A)? 2 2 dt – F is not constant, depends on v a 2 B 2v dv F =− =m R dt Challenge: Look at energy v = vo e −αt a2 B2 where α = mR Claim: The decrease in kinetic energy of Claim: loop is equal to the energy dissipated as heat in the resistor. Can you verify?? heat Physics 212 Lecture 17, Slide 28 28 ...
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This note was uploaded on 02/09/2012 for the course PHYSICS 212 taught by Professor Mestre during the Spring '11 term at University of Illinois at Urbana–Champaign.

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