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Unformatted text preview: ConcepTest: Lenz’s Law
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 current 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 current Upward flux through loop decreases, so need to create upward field Flux into loop is increasing, so need to create field out of loop PHY2049: Chapter 30 24 ConcepTest: Induced Currents
Wire #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 Voltage doubles, but R also (b) I2 = 2 I1 doubles, leaving current the same (c) I1 = I2 0 (d) I1 = I2 = 0 (e) Depends on the strength of the magnetic field PHY2049: Chapter 30 25 Motional EMF
Consider a conducting rod moving on metal rails in a uniform magnetic field: d ( BA) d ( BLx ) dx E= = = = BL = BLv dt dt dt dt
B d Current will flow counter-clockwise in this “circuit”. Why? xxxxxxxxx xxxxxxxxx xxxxxxxxx xxxxxxxxx xxxxxxxxx v L E = BLv x PHY2049: Chapter 30 26 Force and Motional EMF
Pull conducting rod out of B field Current is clockwise. Why? Current within B field causes force Force opposes pull (RHR) Also follows from Lenz’s law We must pull with this force to maintain constant velocity PHY2049: Chapter 30 27 Power and Motional EMF
Force required to pull loop: Power required to pull loop: Energy dissipation through resistance Same 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 it PHY2049: Chapter 30 28 Example
Pull 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 = 10-4 m2 R = L/A = 2.75 x 10-8 * 1.2 / 10-4 = 3.3 x 10-4 EMF Current Force
74 lbs! Power About 0.330 C per sec (from specific heat, density)
PHY2049: Chapter 30 29 Electric Generators
Rotate a loop of wire in a uniform magnetic field:
Changing changing flux induced emf B = BA cos = BA cos t Rotation: =t PHY2049: Chapter 30 30 Electric Generators
Flux is changing in a sinusoidal manner
Leads to an alternating emf (AC generator) d cos( t ) E =N = NBA = NBA sin( t ) dt dt
This is how electricity is generated Water or steam (mechanical power) turns the blades of a turbine which rotates a loop Mechanical power converted to electrical power
PHY2049: Chapter 30 31 d ConcepTest: Generators
A 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?
(a) Increases (b) Decreases (c) Stays the same (d) Varies sinusoidally E = NBA sin( t ) PHY2049: Chapter 30 32 ...
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