Lectures_Lect17

# Lectures_Lect17 - Physics 212 Faraday's Law d B emf = E d =...

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Unformatted text preview: Physics 212 Faraday's Law d B emf = E d = - dt Lecture 17 Physics 212 Lecture 17, Slide 1 Plan Introduce Faraday's Law Show how Faraday's Law explains motional emf examples Stress genesis of new theory Remember, we started from Faraday's Law predicts (correctly) induced emf for cases where there is no motional emf ! F = qv B thinking about what happens in a wire loop Today we state the implications in a very general way Physics 212 Lecture 17, Slide 2 Faraday's Law: d B emf = E d = - dt where 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 Physics 212 Lecture 17, Slide 3 Faraday's Law: In Practical Words: d B emf = E d = - dt where B B dA 1) When the flux B through a loop changes, an emf is induced in the loop. B Flux A Think of B as the number of field lines passing through the surface There are many ways to change this... S h o w P ro je c tio n Physics 212 Lecture 17, Slide 4 Faraday's Law: In Practical Words: d B emf = E d = - dt where B B dA 1) When the flux B through a loop changes, an emf is induced in the loop. B Change the B field A Physics 212 Lecture 17, Slide 5 Faraday's Law: In Practical Words: d B emf = E d = - dt where B B dA 1) When the flux B through a loop changes, an emf is induced in the loop. B Move loop to a place where the B field is different A Physics 212 Lecture 17, Slide 6 Faraday's Law: In Practical Words: d B emf = E d = - dt where B B dA 1) When the flux B through a loop changes, an emf is induced in the loop. B Rotate the loop A Physics 212 Lecture 17, Slide 7 Faraday's Law: In Practical Words: d B emf = E d = - dt where B B dA 1) When the flux B through a loop changes, an emf is induced in the loop. B Rotate the loop A Physics 212 Lecture 17, Slide 8 Faraday's Law: In Practical Words: d B emf = E d = - dt where B B dA 1) When the flux B through a loop changes, an emf is induced in the loop. B Rotate the loop A Physics 212 Lecture 17, Slide 9 Faraday's Law: In Practical Words: d B emf = E d = - dt where B B dA 1) When the flux B through a loop changes, an emf is induced in the loop. 2) The emf will make a current flow if it can (like a battery). I Demo Coil and magnet Physics 212 Lecture 17, Slide 10 A copper loop is placed in a uniform magnetic field as shown. You are looking from the right. Checkpoint 1a Suppose the loop is moving to the right. The current induced in the loop is: A. zero B. clockwise C. counterclockwise Motional emf is ZERO v X B = 0 no charge separation no E field no emf The flux is NOT changing B does not change the area does not change the orientation of B and A does not change Physics 212 Lecture 17, Slide 11 A copper loop is placed in a uniform magnetic field as shown. You are looking from the right. Checkpoint 1b Looking from right X X X X X X X X Now suppose the that loop is stationary and that the magnetic field is Checkpoint 1b decreasing in time. The current induced in the loop is: A. zero B. clockwise C. counterclockwise X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X X Motional emf is ZERO There is no motion of conduction electrons ! HOWEVER: The flux IS changing B decreases in time current induced to oppose the flux change clockwise current tries to restore B that was removed THIS IS NEW !! Faraday's Law explains existence of emf when the motional emf is ZERO! Clockwise current tries to restore B Physics 212 Lecture 17, Slide 12 Now suppose that the loop is spun around a vertical axis as shown, and that it makes one complete revolution every second. Checkpoint 1c The current induced in the loop: A. Is zero B. Changes direction once per second C. Changes direction twice per second Current changes direction every time the loop becomes perpendicular with the B field emf ~ d/dt (B dA = max) d/dt (B dA ) = 0 X O B dA O B X dA Physics 212 Lecture 17, Slide 13 Faraday's Law: In Practical Words: d B emf = E d = - dt where B B dA 1) When the flux B through a loop changes, an emf is induced in the loop. 2) The emf will make a current flow if it can (like a battery). 3) The current that flows induces a new magnetic field. I Physics 212 Lecture 17, Slide 14 Faraday's Law: In Practical Words: d B emf = E d = - dt where B B dA 1) When the flux B through a loop changes, an emf is induced in the loop. 2) The emf will make a current flow if it can (like a battery). 3) The current that flows induces a new magnetic field. 4) The new magnetic field opposes the change in the original magnetic field that created it. (Lenz' Law) B dB/dt Physics 212 Lecture 17, Slide 15 Faraday's Law: In Practical Words: d B emf = E d = - dt where B B dA 1) When the flux B through a loop changes, an emf is induced in the loop. 2) The emf will make a current flow if it can (like a battery). 3) The current that flows induces a new magnetic field. 4) The new magnetic field opposes the change in the original magnetic field that created it. (Lenz' Law) B Demo dB/dt Physics 212 Lecture 17, Slide 16 Faraday's Law: d B emf = E d = - dt where B B dA Executive Summary: emfcurrentfield a) induced only when flux is changing b) opposes the change Physics 212 Lecture 17, Slide 17 A horizontal copper ring is dropped from rest directly above the north pole of a permanent magnet Checkpoint 2 F X B B (copper is not ferromagnetic) Will the acceleration a of the falling ring in the presence of the magnet be any different than it would have been under the influence of just gravity (i.e. g)? A. a > g B. a = g C. a < g Like poles repel Ftotal < mg a < g O This one is hard ! B field increases upward as loop falls Clockwise current (viewed from top) is induced Physics 212 Lecture 17, Slide 18 A horizontal copper ring is dropped from rest directly above the north pole of a permanent magnet Checkpoint 2 HO W IT WO R KS Looking down B (c o p p e r is no t fe rro m a g ne tic ) Will the acceleration a of the falling ring in the presence of the magnet be any different than it would have been under the influence of just gravity (i.e. g)? A. a > g B. a = g C. a < g I I B IL X B points UP Ftotal < mg a < g T h is o ne is h a rd ! B fie ld inc re a s e s up wa rd a s lo o p fa lls C lo c kwis e c urre nt (vie we d fro m to p ) is ind uc e d Main Field produces horizontal forces "Fringe" Field produces vertical force Demo ! dropping magnets e-m cannon Physics 212 Lecture 17, Slide 19 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 b x x x x x x x x x x x x x x x x x x x x x x x x x x x x x y 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 20 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 a v0 emf = - y d B dt B b x x x x x x x x x x x x x x x x x x x x x x x x x x x x x What is the magnitude of the emf induced in the loop just after it enters the field? (A) = Babv02 (B) = Bav0 (C) = Bbv0 (D) = Bav0 (E) = Bbv0 (A) (B) (C) (D) (E) B x x x x x x x b x x x x x x x a x x x x x x x x x x x x x x x y a v0 Change in Flux = dB = BdA = Bav0dt In a time dt it moves by v0dt The area in field changes by dA = v0dt a d B = Bavo dt Physics 212 Lecture 17, Slide 21 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 a v0 emf = - y d B dt B b x x x x x x x x x x x x x x x x x x x x x x x x x x x x 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 (A) (B) (C) emf is induced in direction to oppose the change in flux that produced it y a v0 B b x x x x x x x x x x x x x x x x x x x x x x x x x x x x x Flux is increasing into the screen Induced emf produces flux out of screen Physics 212 Lecture 17, Slide 22 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 a v0 emf = - y d B dt B b x x x x x x x x x x x x x x x x x x x x x x x x x x x x 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 (A) (B) (C) Force on a current in a magnetic field: y F = IL B b a B x x x x x x x v0 I x x x x x x x Force on top and bottom segments cancel (red arrows) Force on right segment is directed in x direction. x Physics 212 Lecture 17, Slide 23 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 a v0 emf = - y d B dt B b x x x x x x x x x x x x x x x x x x x x x x x x x x x x x What is the magnitude of the net force on the loop just after it enters the field? 2 F = 4aBvo R (A) (B) (C) (D) B 2vo / R (A) (B) (C) = a 2 F F = a 2 Bvo R F = IL B = Bav0 F = a 2 B 2vo / R F = IL B y F = ILB since L B b a B F x x x x x x x v0 I x x x x x x x Bavo I= = R R x B 2 a 2vo Bavo F = aB = R R ILB Physics 212 Lecture 17, Slide 24 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 a direction. What is the velocity of the loop when half of it is in the field? FollowUp y t = dt: = Bav0 B x x x x x x x x x x x x x x x x x x x x x x x x x x x x x b v0 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) (B) (C) X X X This is not obvious, but we know v must decrease Why? a b Fright B x x x x x x x v0 I x x x x x x x Fright points to left Acceleration negative Speed must decrease Physics 212 Lecture 17, Slide 25 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? FollowUp y b a v0 B x x x x x x x x x x x x x x x x x x x x x x x x x x x x = 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)v / R = m dv F=a B Why (D), not (A)? 2 2 dt F is not constant, depends on v a 2 B 2v dv F =- =m R dt v = vo e -t where a2B2 = 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 26 ...
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