Announcements Professor Reitze taking over for the rest of the semester Occasional classes by Professor Kumar WebAssign HW Set 7 due the Friday Problems cover material from Chapters 20 and 21 Tea and Cookies with Professor Kumar Tuesday at 5 pm, room 2165 QUESTIONS? PLEASE ASK! Review: Magnetic Flux, EMF Magnetic flux: Φ = A = A cos θ Induced EMF comes from the change in the magnetic flux Faraday s Law ΔΦ ε = N Δt The minus sign - is important: Lenz s Law! The induced EMF sets up a current that opposes the change in magnetic flux it fights back!! Will say more in today s lecture 20.3 Motional EMF Motional EMF Suppose a straight conductor of length l moves perpendicularly with constant velocity through a uniform field The electrons in the conductor experience a magnetic force Recall F M = q v The electrons move down and pile up at the bottom of the conductor, leaving a net positive charge at the top of the conductor As a result of this charge separation, an E field (and F E = qe is produced) Electrons continue to move down until F M = F E q v = q E E = v leading to a potential difference, ΔV, across the conductor ΔV = E l = l v The top is at a higher potential 1
Motional EMF in a Circuit Now place the conductor on a pair of rails and pull it with an applied force F app assume the moving bar has negligible resistance The magnetic force F app on the charges sets up an induced current the charges are free to move in the closed path! Motional emf in a Circuit, cont The changing magnetic flux through the loop and the corresponding induced emf in the bar result from the change in area of the loop The induced motional EMF acts like a battery in the circuit v l ε = vandi l = R 20.4 Lenz Law Revisited Lenz Law Revisited, Conservation of Energy Current due to the induced EMF travels in the direction that creates a magnetic field with flux opposing the change in the original flux through the circuit In the diagram to the right, is decreasing with time φ is decreasing; current I is induced in counterclockwise direction to increase φ If were increasing with time, then the induced current would travel in the clockwise direction When applying Lenz Law, there are two magnetic fields to consider The external changing magnetic field that induces the current in the loop The magnetic field produced by the current in the loop Assume the induced current I is clockwise in the figure The magnetic force F m on the bar would be to the right F m causes bar to accelerate v would increase Magnetic flux φ would increase Current I would increase in clockwise direction A perpetual motion machine?? Sorry Violation of conservation of energy is not allowed!! Thus, current I is counterclockwise 2
20.5 Generators AC Generators, mathematics Alternating Current (AC) generator Converts mechanical energy to electrical energy using induction Consists of a wire loop rotated by some external means falling water (hydroelectric), heat by burning coal to produce steam (coalfired), nuclear fission reaction asic AC generator operation Loop rotates from external force, Magnetic flux through the loop changes with time, inducing an EMF and a current in the external circuit The ends of the loop are connected to slip rings that rotate with the loop Connections to the external circuit are made by stationary brushes in contact with the slip rings The emf generated by the rotating loop can be found by: ε =2 l v =2 l v sin θ If the loop rotates with a constant angular speed, ω, and N turns: θ = ω t v = r ω = (a/2) ω A = l a ε = N A ω sin ω t a/2 Problem (20.37, p 693) Motors and ack EMF In a model AC generator, a 500 turn rectangular coil 8.0 cm by 20 cm rotates at 120 rev/min in a uniform magnetic field of 0.60 T (a)what is the maximum EMF induced in the coil? (b)what is the instantaneous value of EMF in the coil at t = (π/32) s? Assume the EMF is zero at t = 0 (c)what is the smallest value of t for which the EMF will have its maximum value? Motors convert electrical energy into mechanical energy A motor is a generator run in reverse ack EMF is the self-induced EMF that tends to reduce the applied current When a motor is turned on, no back EMF initially The current is very large because it is limited only by the resistance of the coil x x x x x x x x x 3
Motors and ack EMF As the coil begins to rotate, the induced back emf opposes the applied voltage 20.6 Self-inductance Self-inductance occurs when the changing flux through a circuit arises from the circuit itself The current in the coil is reduced The power requirements for starting a motor and for running it under heavy loads are greater than those for running the motor under average loads ω x x x x x x x x x The self-induced EMF must be proportional to the time rate of change of the current ΔI ε = L Δt L is inductance of the device The negative sign is important! It indicates that a changing current induces an EMF in opposition to that change Self-inductance The inductance of a coil depends on geometric factors The SI unit of self-inductance is the Henry 1 H = 1 (V s) / A The expression for L is ΔΦ NΦ = = L N Δ I I 4