Lect17 - Physics 212 Lecture 17 Faraday’s Law dΦB ∫ E...

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Unformatted text preview: Physics 212 Lecture 17 Faraday’s Law dΦB ∫ E ⋅ dl = − dt 50 40 30 20 10 0 Confused Avg = 2.8 Confident Physics 212 Lecture 17, Slide 1 Music Who is the Artist? A) B) C) D) E) Stephane Grappelli Pearl Django Pearl Django Mark O’Connor’s Hot Swing Trio Miles Davis Cassandra Wilson Incredible Album !! Mark O’Connor Connor Wynton Marsalis Jane Monheit Jane Monheit fiddle fiddle trumpet vocals Physics 212 Lecture 17, Slide 2 Physics 212 Lecture 17 Faraday’s Law dΦB ∫ E ⋅ dl = − dt 50 40 30 20 10 0 Confused Avg = 2.8 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 Faraday dΦB emf = ∫ E ⋅ dl = − dt Φ B = ∫ B ⋅ dA Looks scary but it’s not – its amazing and beautiful ! Looks 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 Faraday dΦB emf = ∫ E ⋅ dl = − dt 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 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 Faraday dΦB emf = ∫ E ⋅ dl = − dt 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 Faraday dΦB emf = ∫ E ⋅ dl = − dt 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 Faraday dΦB emf = ∫ E ⋅ dl = − dt 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 Faraday dΦB emf = ∫ E ⋅ dl = − dt 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 Faraday dΦB emf = ∫ E ⋅ dl = − dt 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 Faradays Law Faradays dΦB emf = ∫ E ⋅ dl = − dt Φ B = ∫ B ⋅ dA In Practical Words: In 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 Physics 212 Lecture 17, Slide 12 12 Faraday’s Law Faraday dΦB emf = ∫ E ⋅ dl = − dt 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 Faradays Law Faradays dΦB emf = ∫ E ⋅ dl = − dt 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. that B dB/dt Physics 212 Lecture 17, Slide 14 14 Faradays Law Faradays dΦB emf = ∫ E ⋅ dl = − dt 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. field. B Demo dB/dt Physics 212 Lecture 17, Slide 15 15 Faraday’s Law Faraday dΦB emf = ∫ E ⋅ dl = − dt Φ B = ∫ B ⋅ dA Executive Summary: emf→current→field a) induced only when flux is changing emf 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 50 • HOWEVER: The flux IS changing • B decreases in time 40 • current induced to oppose the flux change 30 • clockwise current puts back B that was 20 clockwise removed removed 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 ! 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 dΦB emf = dt Calculation 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. a v0 B bxxxxxxx xxxxxxx xxxxxxx xxxxxxx x BB 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 xxxxxxx xxxxxxx dA a x In a time dt In dt it moves by v0dt it Change in Flux = dΦB = BdA = Bav0dt Change BdA dΦB = Bav0 dt The area in field The changes by dA = v0dt a dA dt Physics 212 Lecture 17, Slide 23 23 dΦB emf = dt 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 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 dΦB = Bav0 dt The area in field The changes by dA = v0dt a dA dt Physics 212 Lecture 17, Slide 24 24 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. y a BB v0 dΦB emf = 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 25 25 Calculation 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 dΦB emf = 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: 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 26 26 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 = 4aBv0 R (B) F = a 2 Bv0 R (A) (C) F = a 2 B 2v0 2 / R y a BB BB v0 dΦB emf = dt B bxxxxxxx xxxxxxx xxxxxxx xxxxxxx x F = IL × B ε = Bav0 (D) F = a 2 B 2v0 / R F = ILB since L ⊥ B F = IL × B y b a F B xxxxxxx v0 I ε Bav0 I= = R R xxxxxxx a 2 B 2v0 Bav0 F = aB = R R ILB x 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 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 28 28 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 v0 B xxxxxxx xxxxxxx xxxxxxx xxxxxxx ε = Bav0 What is the velocity of the loop when half of it is in the field? 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 ? (A) (D) • Why (D), not (A)? – F is not constant, depends on v F = a 2 B 2v / R = m Challenge: Look at energy dv dt v = v0e −α t B 2a 2 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 29 29 ...
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