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0. 20 Overview. current magnetic field magnetic field current Laws of Faraday & Lenz transformers & power transmission Homework: 4, 9, 15, 19, 26, 45, 55, 69, 78. 0. Motional EMF. magnetic force on free charges creates voltage across rod qE = qvB E = vB EL = vBL - PowerPoint PPT Presentation
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1
20 Overview
• current magnetic field• magnetic field current• Laws of Faraday & Lenz• transformers & power transmission
• Homework:• 4, 9, 15, 19, 26, 45, 55, 69, 78.
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Motional EMF
• magnetic force on free charges creates voltage across rod
• qE = qvB• E = vB • EL = vBL • emf = vBL
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A (d = 1m) bar moves (v = 20 m/s) as shown. (B = 0.25 T). Calculate the emf and the current in the resistor (R = 5.0 Ω).
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Magnetic Flux
• Motional emf works for straight wires, but not for loops
• Solution: Magnetic Flux Concept• Faraday’s Law: Voltage induced in loop
equals the _______ the Magnetic Flux• ______________.• Magnetic Flux is a field x area product• Unit: T·m2
•
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Magnetic Flux Concept
• Method: Draw field lines & loop• Flux is the # lines passing thru loop• Draw the change• Voltage ~ rate of change in # lines thru
loop
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Calculating B-Flux
cos BAB
Ex. B = 1.0T, Area = 10. sq.m., angle = 30 degrees.
22 7.830cos).10)(0.1( mTmTB
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Faraday’s Law
tNVoltage B
N is number of turns of wire on loop. Ex. 50 turns of wire has:
smT
tB
210 2
voltssTmVoltage 250550 2
(1 T·m2 /s = 1 volt)
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What motions produce a change in flux thru the single loop?
If the single loop is moved to the right, what is the direction of the current induced in it?
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Which of the following can produce a changing magnetic flux?
1) B change2) Area change3) angle change4) none of these5) all of these
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Lenz’s Law
• induced voltage opposes the change which produced it
• Ex: A magnet moving in or out of a coil feels a magnetic force which opposes the motion of the magnet
• Ex. Lenz Law Tube
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Ex. A 1.0 sq.m. loop has 60 turns. Its normal is parallel to a uniform B-field of strength 0.10 T. It is rotated so its normal is perpendicular to B in a time of 1.0s. Calculate the voltage induced.
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Applications of Faraday’s Law
• Pick up coils• Generators
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Alternating Current (AC) Generators
• Coil rotates at ω = θ/t (θ = ωt)• Rotation flux change• Voltage = NBAωsin(ωt)
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a) What must be the magnetic field strength so that a generator consisting of 1000 turns of a coil of radius 25 cm produces a peak output of 160 V when turned at a frequency of 60 Hz? b) Sketch a graph of the output of the generator.
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Transformers• Flux & ΔΦB/Δt _________
for each coil• By Faraday’s Law:• Vp = Np ΔΦB/Δt and
• Vs = Ns ΔΦB/Δt
s
p
s
p
NN
VV
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Power and Current in Transformers
• Conservation of Energy implies power at primary is the same as power at secondary:
• ______________
• Ex: A transformer increases voltage by a factor of ten, the output (secondary) current decreases by a factor of ten:
1010p
p
pp
s
pps
IVV
IVV
II
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Electromagnetic Waves• Faraday: time varying B produces time
varying E• Maxwell: time varying E produces time
varying B• i.e. one begets the other & self-sustaining,
time-varying EM wave is produced
Polarization• overall orientation of electric field of light• simplest cases: unpolarized (radial), plane
polarized (linear)
Polarizing Filters• Polarizing material
allows the passage of only one direction of E
• Malus’ Law:2
0 cosI I
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Properties of Electromagnetic Waves
• travel in vacuum• transverse waves• speed in a vacuum governed by magnetic
and electric constants of free space
• c = f = 299,792,458 m/s (3.00 x 108 m/s)
00
1
c
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Spectrum by Wavelength• microwaves: cm range waves strongly absorbed by water.
cold spots separated by half-wavelength• infrared (IR): ~mm to um waves also strongly absorbed by
water• radio waves: wavelengths ~ 1 to 500 meters• Ex. f = 100 MHz. What is its wavelength?• visible: ~ 400 to 700 nm (400 is violet, 700 is red)• ultraviolet (UV): ~ 0.1 to 100 nm, causes sunburn• x-ray: ~ 0.01 to 0.001 nm waves can pass through 10cm of
many materials• gamma-rays: < 0.001 nm waves are even more penetrating
Standing Waves• Confined microwaves
create a standing wave
• Hot spots are separated by half a wavelength
• Most microwave ovens are around 2400MHz
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Chapter Summary• moving conductor in a B field gets a
motional emf.• Faraday’s Law: emf = -t • Lenz’s Law: energy conservation• generators & motors utilize F = ILB,
experience back emf• transformers step ac voltages up or down• EM waves: E & B oscillation
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Intensity
• wave intensity in watts/square-meter:
• Ex. 5 mW laser is focused to a spot size of diameter 1.0 mm.
AreaPower
timeAreaEnergyS
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Intensity for Different Types of Waves
• Plane Waves – Intensity is constant• Spherical Waves – Intensity falls off as
inverse square
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Energy in EM Waves
• E = cB• u = ε0 E2 = (1/μ0)B2
• Intensity S = cu = cε0E2 = (c/μ0)B2
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Ex. A laser beam has a peak intensity of 150 W/m2. Find the amplitude of the electric and magnetic fields.
•S = cu = cε0E2 = (c/μ0)B2
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Eddy Currents• Current induced in metal due to magnetic
fields
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calculating emf for loops
• summary:• draw magnetic field lines • count the number of penetrating lines (#
that pass through the loop) at two (or more) times
• the emf induced is ~ to the change in # of penetrating lines per second
• # penetrating lines ~ “magnetic flux”
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A metallic wire loop is in a uniform magnetic field.
How does the flux change if: a)ring moves a little to left or right?b)ring begins to rotate?
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Producing B and E Fields
• Electrical current creates B• Changing B field creates a circulating E
field.• This E field creates the circulating currents
observed in wire loops.
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Back emf
• rotating coil in motor experiences an induced emf opposite to battery’s V
• net voltage = V – back-emf = IR• I = current in motor• R = resistance of motor coil• back-emf ~ speed of coil, therefore is zero
when motor starts (or freezes)• current is large when back-emf is small
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Direct Current (DC) Generators
• split ring keeps current flowing in only one direction
• output can be smoothed
120 V ac is applied across the primary of a step down transformer with turns ratio 1/50. How does the power applied at the primary compare to that at the secondary? (Assume a lossless transformer)
1. Reduced by a factor of 502. Increased by a factor of 503. It is the same4. Not enough information
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Application to Power Generation
• Higher voltage transmission reduces resistive heat loss (I2R).
• Ex. Power transmitted thru 10m long wire which has 1 ohm resistance.
• At 6V: Current = V/R = 6V/1ohm = 6A• At 60V: Current = V/R = 60V/1ohm = 6A