15PHY2054: Chapter 20Reading Quiz 4Î Faraday’s law says that1. an emf is induced in a loop when it moves through an electric field2. the induced emf produces a current whose magnetic field opposes the original change3. the induced emf is proportional to the rate of change of magnetic fluxFaraday’s law16PHY2054: Chapter 20ConcepTest: Lenz’s Law ÎIf a North pole moves towards the loop from above the page, in what direction is the induced current?  (a) clockwise  (b) counter-clockwise  (c) no induced currentMust counter flux change indownward direction with upward B field17PHY2054: Chapter 20ConcepTest: Induced Currents ÎA wire loop is being pulled through a uniform magnetic field. What is the direction of the induced current? (a) clockwise  (b) counter-clockwise  (c) no induced currentx x x x x x x x x x x x xx x x x x x x x x x x x xx x x x x x x x x x x x xx x x x x x x x x x x x xx x x x x x x x x x x x xx x x x x x x x x x x x xx x x x x x x x x x x x xNo change in flux, no induced current18PHY2054: Chapter 20ConcepTest: Induced Currents In the cases above, what is the direction of the induced current?x x x x x x x x x x x x x x x x x x x x x x x x xx x x x x x x x x x x x x x x x x x x x x x x x xx x x x x x x x x x x x x x x x x x x x x x x x xx x x x x x x x x x x x x x x x x x x x x x x x xx x x x x x x x x x x x x x x x x x x x x x x x xx x x x x x x x x x x x x x x x x x x x x x x x xx x x x x x x x x x x x x x x x x x x x x x x x xx x x x x x x x x x x x x x x x x x x x x x x x x12CounterclockwiseNone19PHY2054: Chapter 20ConcepTest: Lenz’s Law ÎIf a coil is shrinking in a B field pointing into the page, in what direction is the induced current?  (a) clockwise  (b) counter-clockwise  (c) no induced currentDownward flux is decreasing,so need to create downwardB field20PHY2054: Chapter 20Induced currents ÎA circular loop in the plane of the paper lies in a 3.0 T magnetic field pointing into the paper. The loop’s diameter changes from 100 cm to 60 cm in 0.5 s What is the magnitude of the average induced emf? What is the direction of the induced current? If the coil resistance is 0.05Ω , what is the average induced current? Direction = clockwise (Lenz’s law) Current = 3.016 / 0.05 = 60.3 A()220.3 0.53.0 3.016 Volts0.5BVtπ−ΔΦ==× =Δ21PHY2054: Chapter 20ConcepTest: Induced Currents ÎA wire loop is pulled away from a current-carrying wire. What is the direction of the induced current in the loop? (a) clockwise  (b) counter-clockwise  (c) no induced current IDownward flux through loopdecreases, so need to createdownward field22PHY2054: Chapter 20ConcepTest: Induced Currents ÎA wire loop is moved in the direction of the current. What is the direction of the induced current in the loop? (a) clockwise  (b) counter-clockwise  (c) no induced current IFlux does not change whenmoved along wire23PHY2054: Chapter 20ConcepTest: Lenz’s Law Î If the B field pointing out of the page suddenly drops to zero, in what direction is the induced current?  (a) clockwise  (b) counter-clockwise  (c) no induced currentÎ If a coil is rotated as shown, in a B field pointing to the left, in what direction is the induced current?  (a) clockwise  (b) counter-clockwise  (c) no induced currentUpward flux through loopdecreases, so need to createupward fieldFlux into loop is increasing, soneed to create field out of loop24PHY2054: Chapter 20ConcepTest: Induced CurrentsÎWire #1 (length L) forms a one-turn loop, and a bar magnet is dropped through. Wire #2 (length 2L) forms a two-turn loop, and the same magnet is dropped through. Compare the magnitude of the induced currents in these two cases. (a) I1= 2 I2 (b) I2= 2 I1 (c) I1= I2≠ 0 (d) I1= I2= 0 (e) Depends on the strength of the magnetic fieldVoltage doubles, but R alsodoubles, leaving current the same25PHY2054: Chapter 20Motional EMFÎConsider a conducting rod moving on metal rails in a uniform magnetic field: () ( )εΦ== = =BddBA dBLx dxBLdt dt dt dtxx 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 x x xx x x x x x x x x vLε= BLvCurrent will flow counter-clockwise in this “circuit”. Why?26PHY2054: Chapter 20Force and Motional EMFÎ Pull conducting rod out of B fieldÎ Current is clockwise. Why?Î Current within B field causes force Force opposes pull (RHR) Also follows from Lenz’s lawÎ We must pull with this forceto maintain constant velocityε==BLviRR22==BLvFiLBR27PHY2054: Chapter 20Power and Motional EMFÎForce required to pull loop:ÎPower required to pull loop:ÎEnergy dissipation through resistanceÎSame as pulling power! So power is dissipated as heat Kinetic energy is constant, so energy has to go somewhere Rod heats up as you pull it22==BLvFiLBR222==BLvPFvR22222⎛⎞== =⎜⎟⎝⎠BLv B L vPiR RRR28PHY2054: Chapter 20ExampleÎPull a 30cm x 30cm conducting loop of aluminum through a 2T B field at 30cm/sec. Assume it is 1cm thick. Circumference = 120cm = 1.2m, cross sectional area = 10-4m2 R = ρL/A = 2.75 x 10-8* 1.2 / 10-4= 3.3 x 10-4 ΩÎEMFÎCurrentÎForceÎPower20.30.3 0.18Vε==××=BLv4/ 0.18/ 3.3 10 545Aε−== ×=iR298W==PiRAbout 0.330 C per sec(from specific heat, density)545 0.3 2 327 NFiLB==××=74 lbs!29PHY2054: Chapter 20Electric GeneratorsÎRotate a loop of wire in a uniform magnetic field:  changing θ⇒changing flux ⇒ induced emf ΦB= B A cos θ = B A cos(ωt)Rotation: θ = ωt30PHY2054: Chapter 20Electric GeneratorsÎFlux is changing in a sinusoidal manner Leads to an alternating emf (AC generator)cos( )sin( )BddtNNBA NBAtdt dtωωωεΦ== =¾ This is how electricity is generated¾ Water or steam (mechanical power) turns the blades of a turbine which rotates a loop¾ Mechanical power converted to electrical power31PHY2054: Chapter 20ConcepTest: GeneratorsÎA generator has a coil of wire rotating in a magnetic field. If the B field stays constant and the area of the coil remains constant, but the rotation rate increases, how is the maximum output voltage of the generator affected?