1. Exam 3 covers Lecture, Readings, Discussion, HW, Lab
Exam 3 is Tue. Nov. 25, 5:30-7 pm, 2103 Chamberlin (here)
Biot-Savart Law - currents produce magnetic fields
Ampere’s law - shortcut to determining mag. fields from currents.
Magnetic flux, Faraday effect, Lenz’ law
Electromagnetic waves:
Wavelength, freq, speed
E&B fields, intensity, power, rad. pressure, Poynting vec
Polarization
Modern Physics (quantum mechanics)
Photons & photoelectric effect
Bohr atom: Energy levels, absorbing & emitting photons

2. Law of Biot-Savart
B out of page
Each element of current produces a contribution to the magnetic field. r  I ds dI dB r

3. Field from a circular loop
Each current element produce dB
All contributions add as vectors
Along axis, all components cancel except for x-comp

4. Magnetic field from loopBz
Which of these graphs best represents the magnetic field on the axis of the loop? A. z Bz B. z z x y Bz C. z Bz D. z

5. Ampere’s law Sum up component of B around path
Equals current through surface.
Component of B along path I
closed path
Ampere’s law
surface bounded by path

6. Quick Quiz
A long wire of radius R carries a current uniformly through its cross-section. How does the B-field at R compare to that at R/2?
BR=BR/2
BR=2BR/2
BR=BR/2/2
BR=4BR/2 r B R

7. Ampere’s law for the solenoid

8. Time-dependent fields
Faraday effect
Changing magnetic flux induces EMF
Displacement current
Changing electric flux induces B-field
Electromagnetic waves
E-field and B-field both changing in time
Each ‘induces’ the other
Propagating E- and B-fields

9. Magnetic flux Faraday’s law
Magnetic flux is defined exactly as electric flux
(Component of B  surface) x (Area element)
Faraday’s law
Magnetic flux through surface bounded by path
EMF around loop
Time derivative
Make comparison to battery. Show that this acts just like battery. Maybe use shaking flashlight to show that this works.
If path along conducting loop, induces current I=EMF/R

10. Quick quiz
Which of these conducting loops will have currents flowing in them? A. C.
Constant I
I(t) increases
Talk about magnetic fields generated by the induced currents, and what sense magnet that produces. B. D.
Constant v
Constant v
Constant I
Constant I

11. Lenz’s law & forces Induced current produces a magnetic field.
Interacts with bar magnet just as another bar magnet
Lenz’s law
Induced current generates a magnetic field that tries to cancel the change in the flux.
Here flux through loop due to bar magnet is increasing. Induced current produces flux to left.
Force on bar magnet is to left.
Do demo with magnet and copper plate. Copper plate in nitrogen.

12. Quick Quiz Left Right Up Down Into page Out of page
A person moves a conducting loop with constant velocity away from a wire as shown. The wire has a constant current What is the direction of force on the loop from the wire? I
Left
Right Up
Down
Into page
Out of page v
cancel
Force is up

13. Quick Quiz
A square loop rotates at frequency f in a 1T uniform magnetic field as shown. Which graph best represents the induced current (CW current is positive)?
B=1T A. C. B. D.
=0 in orientation shown

14. Inductance: a general result
Flux = (Inductance) X (Current)
Change in Flux = (Inductance) X (Change in Current)
Faraday’s law:

15. Energy stored in ideal inductor
Constant current (uniform charge motion)
No work required to move charge through inductor
Increasing current:
Work required to move charge across induced EMF
Total work
Energy stored in inductor

16. RL circuits - I? + Current decreases in time Time constant
Slow for large inductance
(inductor fights hard, tries to keep constant current)
Slow for small resistance
(no inductor EMF needed to drive current)
Time constant

17. Electromagnetic waves
In empty space: sinusoidal wave propagating along x with velocity
E = Emax cos (kx – ωt)
B = Bmax cos (kx – ωt) λ
E and B are perpendicular oscillating vectors
The direction of propagation is
perpendicular to E and B

18. Quick Quiz on EM waves z c E B y x

19. Power and Intensity Radiation Pressure
EM wave transports energy at its propagation speed.
Instantaneous power/area = |Poynting vector|=
Intensity = Average power/area =
Spherical wave:
Radiation Pressure
EM wave incident on surface exerts a radiation pressure prad (force/area) proportional to intensity I.
Perfectly absorbing (black) surface:
Perfectly reflecting (mirror) surface:
Resulting force = (radiation pressure) x (area)

20. Polarization Linear polarization: Linear polarizer:
E-field oscillates in fixed plane of polarization
Linear polarizer:
Transmits component of E-field parallel to transmission axis
Absorbs component perpendicular to transmission axis.
Intensity
Circular Polarization
E-field rotates at constant magnitude

21. Quantum Mechanics Light comes in discrete units:
Photon energy
Demonstrated by Photoelectric Effect
Photon of energy hf collides with electron in metal
Transfers some or all of hf to electron
If hf >  (= workfunction) electron escapes
Electron ejected only if hf > 
Minimum photon energy required

22. Photon properties of light
Photon of frequency f has energy hf
Red light made of ONLY red photons
The intensity of the beam can be increased by increasing the number of photons/second.
(#Photons/second)(Energy/photon) = energy/second = power

23. Photon energy What is the energy of a photon of red light (=635 nm)?
0.5 eV
1.0 eV
2.0 eV
3.0 eV

24. Bohr’s model of Hydrogen atom
Planetary model: Circular orbits of electrons around proton.
Quantization
Discrete orbit radii allowed:
Discrete electron energies:
Each quantum state labeled by quantum # n
How did he get this?
Quantization of circular orbit angular mom.

25. Consequences of Bohr model
Electron can make transitions between quantum states.
Atom loses energy: photon emitted
Photon absorbed: atom gains energy:

26. Wavelength is smaller for larger jump!
Spectral Question
Compare the wavelength of a photon produced from a transition from n=3 to n=1 with that of a photon produced from a transition n=2 to n=1.
A. λ31 < λ21
B. λ31 = λ21
C. λ31 > λ21
n=2
n=3
n=1
E31 > E21 so λ31 < λ21
Wavelength is smaller for larger jump!

27. Question
This quantum system (not a hydrogen atom) has energy levels as shown. Which photon could possibly be absorbed by this system?
E3=7 eV
E3=5 eV
A nm
B. 413 nm
C. 310 nm
D. 248 nm
E2=3 eV
E1=1 eV