1. 20 Overview current  magnetic field magnetic field  current
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
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

7. Calculating B-Flux
Ex. B = 1.0T, Area = 10. sq.m., angle = 30 degrees.

8. Faraday’s Law
(1 T·m2 /s = 1 volt)
N is number of turns of wire on loop. Ex. 50 turns of wire has:

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?
B change
Area change
angle change
none of these
all of these

11. Lenz’s Law induced voltage opposes the change which produced it
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

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:

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

19. Polarization overall orientation of electric field of light
simplest cases: unpolarized (radial), plane polarized (linear)

20. Polarizing Filters
Polarizing material allows the passage of only one direction of E
Malus’ Law:

21. Properties of Electromagnetic Waves
travel in vacuum
transverse waves
speed in a vacuum governed by magnetic and electric constants of free space
c = fl = 299,792,458 m/s (3.00 x 108 m/s)

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 nm waves can pass through 10cm of many materials
gamma-rays: < nm waves are even more penetrating

23. Standing Waves Confined microwaves create a standing wave
Hot spots are separated by half a wavelength
Most microwave ovens are around 2400MHz

24. Chapter Summary moving conductor in a B field gets a motional emf.
moving conductor in a B field gets a motional emf.
Faraday’s Law: emf = -DF/Dt
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.

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
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:
ring moves a little to left or right?
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

35. Increased by a factor of 50 It is the same Not enough information
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)
Reduced by a factor of 50
Increased by a factor of 50
It is the same
Not enough information

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