Lect17 - Physics 212 Faraday’s Law rr dΦB ∫ E ⋅ dl =...

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Unformatted text preview: Physics 212 Faraday’s Law rr dΦB ∫ E ⋅ dl = − dt 50 40 30 20 10 0 Lecture 17 Confused Avg = 2.9 Confident Physics 212 Lecture 17, Slide 1 Physics 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 ! Your comments: So there's this girl in the third row on the left side of the lecture hall that is really cute. I just wanted to say hi, since I'm too shy to actually come up and talk to you. Also, llamas are cool my friend CJS annoys me whenever he talks about how he's going to get a quote of his on that board so could you just put him up there? I'm iffy on everything in this preflight. Physics 212 Lecture 17, Slide 2 Physics Faraday’s Law Faraday rr dΦB emf = ∫ E ⋅ dl = − dt rr Φ B = ∫ B ⋅ dA Looks scary but it’s not – its amazing and beautiful ! A changing magnetic flux produces an electric field. Electricity and magnetism are deeply connected Electricity Physics 212 Lecture 17, Slide 3 Physics Faraday’s Law Faraday In Practical Words: rr dΦB emf = ∫ E ⋅ dl = − dt rr Φ B = ∫ B ⋅ dA 1) When the flux ΦB through a loop changes, an emf is induced in the emf loop. B Flux A Physics 212 Lecture 17, Slide 4 Physics Think of ΦB as the number of field lines passing through the surface There are many ways to change this… Faraday’s Law Faraday In Practical Words: rr dΦB emf = ∫ E ⋅ dl = − dt rr Φ B = ∫ B ⋅ dA 1) When the flux ΦB through a loop changes, an emf is induced in the emf loop. B Change the B field A Physics 212 Lecture 17, Slide 5 Physics Faraday’s Law Faraday In Practical Words: rr dΦB emf = ∫ E ⋅ dl = − dt rr Φ B = ∫ B ⋅ dA 1) When the flux ΦB through a loop changes, an emf is induced in the emf loop. B Move loop to a place where Move the B field is different A Physics 212 Lecture 17, Slide 6 Physics Faraday’s Law Faraday In Practical Words: rr dΦB emf = ∫ E ⋅ dl = − dt rr Φ B = ∫ B ⋅ dA 1) When the flux ΦB through a loop changes, an emf is induced in the emf loop. B Rotate the loop Rotate A Physics 212 Lecture 17, Slide 7 Physics Faraday’s Law Faraday In Practical Words: rr dΦB emf = ∫ E ⋅ dl = − dt rr Φ B = ∫ B ⋅ dA 1) When the flux ΦB through a loop changes, an emf is induced in the emf loop. B Rotate the loop Rotate A Physics 212 Lecture 17, Slide 8 Physics Faraday’s Law Faraday In Practical Words: rr dΦB emf = ∫ E ⋅ dl = − dt rr Φ B = ∫ B ⋅ dA 1) When the flux ΦB through a loop changes, an emf is induced in the emf loop. B Rotate the loop Rotate A Physics 212 Lecture 17, Slide 9 Physics Faradays Law Faradays In Practical Words: rr dΦB emf = ∫ E ⋅ dl = − dt rr Φ B = ∫ B ⋅ dA 1) When the flux ΦB through a loop changes, an emf is induced in the emf loop. 2) The emf will make a current flow if it can (like a battery). emf I Demo Physics 212 Lecture 17, Slide 10 Physics Faraday’s Law Faraday In Practical Words: rr dΦB emf = ∫ E ⋅ dl = − dt rr Φ B = ∫ B ⋅ dA 1) When the flux ΦB through a loop changes, an emf is induced in the loop. emf 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 11 Physics Faradays Law Faradays In Practical Words: rr dΦB emf = ∫ E ⋅ dl = − dt rr Φ B = ∫ B ⋅ dA 1) When the flux ΦB through a loop changes, an emf is induced in the loop. emf 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 flux that created it. opposes B dB/dt Physics 212 Lecture 17, Slide 12 Physics Faradays Law Faradays In Practical Words: rr dΦB emf = ∫ E ⋅ dl = − dt rr Φ B = ∫ B ⋅ dA 1) When the flux ΦB through a loop changes, an emf is induced in the loop. emf 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. B Demo dB/dt Physics 212 Lecture 17, Slide 13 Physics Faraday’s Law Faraday rr dΦB emf = ∫ E ⋅ dl = − dt rr Φ B = ∫ B ⋅ dA Executive Summary: emf→current→field a) induced only when flux is changing b) opposes the change Physics 212 Lecture 17, Slide 14 Physics BB Preflight 2 • Motional emf is ZERO •vXB=0 50 • no charge separation • no E field 40 • 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 15 Physics BB Looking from right XXXXXXXX XXXXXXXX Preflight 4 • Motional emf is ZERO • There is no motion of conduction electrons ! 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 removed and opposes the decrease in 10 flux XXXXXXXX XXXXXXXX XXXXXXXX Clockwise restores B 0 Physics 212 Lecture 17, Slide 16 Physics BB Preflight 6 Current changes direction every time the loop becomes perpendicular with the B field emf ~ dΦ/dt (B ∏ dA = max) fl d/dt (B ∏ dA ) = 0 B dA B dA 70 60 50 40 30 20 10 0 Physics 212 Lecture 17, Slide 17 Physics F BB X O B B Preflight 8 Like poles repel Ftotal < mg a<g 50 40 30 20 10 0 (copper is not ferromagnetic) This one is hard ! B field increases upward as loop falls Clockwise current (viewed from top) is induced Physics 212 Lecture 17, Slide 18 Physics HOW IT WORKS Looking down B Preflight 8 B I I (copper is not ferromagnetic) IL X B points UP Ftotal < mg a<g This one is hard ! B field increases upward as loop falls Clockwise current (viewed from top) is induced Main Field produces horizontal forces Fringe Field produces vertical force Demo ! Physics 212 Lecture 17, Slide 19 Physics 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 direction and the magnitude of the force on the loop when half of it is in the field? Calculation a v0 B bxxxxxxx xxxxxxx xxxxxxx xxxxxxx x y • Conceptual Analysis – – • Strategic Analysis – – – Once loop enters B field region, flux will be changing in time Faraday’s Law then says emf will be induced in loop, making a current flow that opposes the change in flux Find the emf Find the current in the loop Find the force on the current Physics 212 Lecture 17, Slide 20 Physics 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. Calculation y dΦB emf = dt a v0 BB 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 y (B) ε = ½ Bav0 (C) ε = ½ Bbv0 (D) ε = Bav0 (E) ε = Bbv0 dA a v0 B xxxxxxx b xxxxxxx xxxxxxx xxxxxxx x a Change in Flux = dΦB = BdA = Bav0dt dΦB = Bav0 dt In a time dt it moves by v0dt The area in field changes by dA = v0dt a Physics 212 Lecture 17, Slide 21 Physics 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. Calculation y dΦB emf = dt 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 y (B) ε = ½ Bav0 (C) ε = ½ Bbv0 (D) ε = Bav0 (E) ε = Bbv0 a v0 B xxxxxxx b xxxxxxx a xxxxxxx xxxxxxx x Change in Flux = dΦB = BdA = Bav0dt dΦB = Bav0 dt In a time dt it moves by v0dt The area in field changes by dA = v0dt a Physics 212 Lecture 17, Slide 22 Physics 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. Calculation Calculation y a BB v0 B bxxxxxxx xxxxxxx xxxxxxx xxxxxxx dΦB emf = dt x What is the direction of the current induced in the loop just after it enters the field? (A) clockwise (B) counterclockwise (C) no current is induced emf is induced in direction to oppose the change in flux that produced it y a v0 B bxxxxxxx xxxxxxx xxxxxxx xxxxxxx x Flux is increasing into the screen Induced emf produces induced current with flux out of screen Physics 212 Lecture 17, Slide 23 Physics 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. Calculation y BB a v0 B bxxxxxxx xxxxxxx xxxxxxx xxxxxxx dΦB emf = dt x What is the direction of the net force on the loop just after it enters the field? (A) +y (B) -y (C) +x (D) -x r rr 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. x Physics 212 Lecture 17, Slide 24 Physics 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. Calculation y a BB v0 B bxxxxxxx xxxxxxx xxxxxxx xxxxxxx dΦB emf = dt 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 (C) F = a 2 B 2v0 2 / R r rr F = IL × B x ε = Bav0 (D) F = a 2 B 2v0 / R r rr F = IL × B y rr F = ILB since L ⊥ B b a B xxxxxxx v0 I xxxxxxx x F Bav0 I= = R R ε a 2 B 2v0 ⎛ Bav0 ⎞ F =⎜ ⎟ aB = R ⎝R⎠ ILB Physics 212 Lecture 17, Slide 25 Physics 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. What is the velocity of the loop when half of it is in the field? Follow-Up y t = dt: ε = Bav0 b B xxxxxxx xxxxxxx xxxxxxx xxxxxxx x v0 BB 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) X X X This is not obvious, but we know v must decrease Why? b a Fright B xxxxxxx v0 I xxxxxxx Fright points to left Acceleration negative Speed must decrease Physics 212 Lecture 17, Slide 26 Physics 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. What is the velocity of the loop when half of it is in the field? Follow-Up y b a 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 ? (A) (D) • Why (D), not (A)? – F is not constant, depends on v F = a 2 B 2v / R = m dv dt v = v0e −α t B 2a 2 where α = mR Challenge: Look at energy Claim: The decrease in kinetic energy of loop is equal to the energy dissipated as heat in the resistor. Can you verify?? Physics 212 Lecture 17, Slide 27 Physics ...
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