20 overview

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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