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.

2

Motional EMF

• magnetic force on free charges creates voltage across rod

• qE = qvB• E = vB • EL = vBL • emf = vBL

3

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).

4

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

•

5

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

6

7

Calculating B-Flux

cos BAB

Ex. B = 1.0T, Area = 10. sq.m., angle = 30 degrees.

22 7.830cos).10)(0.1( mTmTB

8

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)

9

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?

10

Which of the following can produce a changing magnetic flux?

1) B change2) Area change3) angle change4) none of these5) all of these

11

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

12

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.

13

Applications of Faraday’s Law

• Pick up coils• Generators

14

Alternating Current (AC) Generators

• Coil rotates at ω = θ/t (θ = ωt)• Rotation flux change• Voltage = NBAωsin(ωt)

15

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.

16

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

17

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

18

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

21

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

22

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

23

24

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

25

Intensity

• wave intensity in watts/square-meter:

• Ex. 5 mW laser is focused to a spot size of diameter 1.0 mm.

AreaPower

timeAreaEnergyS

26

Intensity for Different Types of Waves

• Plane Waves – Intensity is constant• Spherical Waves – Intensity falls off as

inverse square

27

Energy in EM Waves

• E = cB• u = ε0 E2 = (1/μ0)B2

• Intensity S = cu = cε0E2 = (c/μ0)B2

28

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

29

Eddy Currents• Current induced in metal due to magnetic

fields

30

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”

31

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?

32

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.

33

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

34

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

35

36

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