Exam 3 covers Lecture, Readings, Discussion, HW, Lab Exam 3 is Thurs. Dec. 3, 5:30-7 pm, 145 Birge Magnetic dipoles, dipole moments, and torque Magnetic flux, Faraday effect, Lenz’ law Inductors, inductor circuits Electromagnetic waves: Wavelength, freq, speed E&B fields, intensity, power, radiation pressure Polarization Modern Physics (quantum mechanics) Photons & photoelectric effect Bohr atom: Energy levels, absorbing & emitting photons Uncertainty principle Tues. Dec. 1, 20091Phy208 Lect. 25

Tues. Dec. 1, 2009Phy208 Lect. 252 Current loops & magnetic dipoles Current loop produces magnetic dipole field. Magnetic dipole moment: current Area of loop magnitude direction In a uniform magnetic field Magnetic field exerts torque Torque rotates loop to align with

Works for any shape planar loop Tues. Dec. 1, 2009Phy208 Lect. 253 I perpendicular to loop Torque in uniform magnetic field Potential energy of rotation: Lowest energy aligned w/ magnetic field Highest energy perpendicular to magnetic field

4 Which of these loop orientations has the largest magnitude torque? Loops are identical apart from orientation. (A) a (B) b (C) c Question on torque a b c Tues. Dec. 1, 2009Phy208 Lect. 25

Magnetic flux Magnetic flux through surface bounded by path EMF around loop Time derivative Faraday’s law If path along conducting loop, induces current I=EMF/R Magnetic flux is defined exactly as electric flux (Component of B  surface) x (Area element) Tues. Dec. 1, 20095Phy208 Lect. 25

Quick quiz Which of these conducting loops will have currents flowing in them? Constant I I(t) increases Constant I Constant v Constant I Constant v A. B. C. D. Tues. Dec. 1, 20096Phy208 Lect. 25

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. Tues. Dec. 1, 20097Phy208 Lect. 25

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  =0 in orientation shown A. B. C. D. Tues. Dec. 1, 20098Phy208 Lect. 25

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. Tues. Dec. 1, 20099Phy208 Lect. 25

Quick Quiz 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? A.Left B.Right C.Up D.Down E.Into page F.Out of page I v Force is up cancel Tues. Dec. 1, Phy208 Lect. 25

Inductors Flux = (Inductance) X (Current) Change in Flux = (Inductance) X (Change in Current) Potential difference Constant current -> no potential diff Tues. Dec. 1, Phy208 Lect. 25

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 Tues. Dec. 1, Phy208 Lect. 25

Tues. Dec. 1, 2009Phy208 Lect ILIL IL(t)IL(t) Time ( t ) 0 0 Slope dI / dt = V battery / L I L instantaneously zero, but increasing in time Inductors in circuits

Just a little later… A short time later ( t=0+Δt ), the current is increasing … Tues. Dec. 1, 2009Phy208 Lect IL(t)IL(t) Time ( t ) 0 0 Slope dI / dt = V battery / L A.More slowly B.More quickly C.At the same rate I L >0, and I R =I L V R ≠0, so V L smaller V L = -LdI/dt, so dI/dt smaller Switch closed at t=0

In empty space: sinusoidal wave propagating along x with velocity E = E max cos (kx –  t) B = B max cos (kx –  t) E and B are perpendicular oscillating vectors The direction of propagation is perpendicular to E and B  Electromagnetic waves Tues. Dec. 1, Phy208 Lect. 25

Quick Quiz on EM waves x z y c E B Tues. Dec. 1, Phy208 Lect. 25

EM wave transports energy at its propagation speed. Intensity = Average power/area = EM wave incident on surface exerts a radiation pressure p rad (force/area) proportional to intensity I. Perfectly absorbing (black) surface: Perfectly reflecting (mirror) surface: Resulting force = (radiation pressure) x (area) Radiation Pressure Power and Intensity Spherical wave: Tues. Dec. 1, Phy208 Lect. 25

Polarization Linear polarization: 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 Tues. Dec. 1, Phy208 Lect. 25

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 Tues. Dec. 1, Phy208 Lect. 25

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 Tues. Dec. 1, Phy208 Lect. 25

Photon energy What is the energy of a photon of red light ( =635 nm)? A.0.5 eV B.1.0 eV C.2.0 eV D.3.0 eV Tues. Dec. 1, Phy208 Lect. 25

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. Tues. Dec. 1, Phy208 Lect. 25

Consequences of Bohr model Electron can make transitions between quantum states. Atom loses energy: photon emitted Photon absorbed: atom gains energy: Tues. Dec. 1, Phy208 Lect. 25

24 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. Spectral Question n=2 n=3 n=1 A.  31 <  21 B.  31 =  21 C.  31 >  21 E 31 > E 21 so  31 <  21 Wavelength is smaller for larger jump! Tues. Dec. 1, 2009Phy208 Lect. 25

Question This quantum system (not a hydrogen atom) has energy levels as shown. Which photon could possibly be absorbed by this system? E 1 =1 eV E 2 =3 eV E 3 =5 eV E 3 =7 eV A nm B. 413 nm C. 310 nm D. 248 nm Tues. Dec. 1, Phy208 Lect. 25

Matter Waves deBroglie postulated that matter has wavelike properties. deBroglie wavelength Example: Wavelength of electron with 10 eV of energy: Kinetic energy Tues. Dec. 1, Phy208 Lect. 25

Tues. Dec. 1, 2009Phy208 Lect Heisenberg Uncertainty Principle Using  x = position uncertainty  p = momentum uncertainty Heisenberg showed that the product (  x )  (  p ) is always greater than ( h / 4  ) Often write this as where is pronounced ‘h-bar’ Planck’s constant