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Exam 3 covers Lecture, Readings, Discussion, HW, Lab

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

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Exam 3 covers Lecture, Readings, Discussion, HW, Lab

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  1. Exam 3 coversLecture, 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 Phy208 Lect. 25

  2. Current loops & magnetic dipoles • Current loop produces magnetic dipole field. • Magnetic dipole moment: Area of loop current direction magnitude In a uniform magnetic field Magnetic field exerts torqueTorque rotates loop to align with Phy208 Lect. 25

  3. Works for any shape planar loop perpendicular to loop Torque in uniform magnetic field I Potential energy of rotation: Lowest energy aligned w/ magnetic field Highest energy perpendicular to magnetic field Phy208 Lect. 25

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

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

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

  7. 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. Phy208 Lect. 25

  8. B=1T 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)? A. C. 0 0 B. D. 0 0 =0 in orientation shown Phy208 Lect. 25

  9. 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. Phy208 Lect. 25

  10. Force is up cancel Quick Quiz • A person moves a conducting loop with constant velocity away from a wire as shown. The wire has a constant currentWhat is the direction of force on the loop from the wire? I Left Right Up Down Into page Out of page v Phy208 Lect. 25

  11. Inductors • Flux = (Inductance) X (Current) • Change in Flux = (Inductance) X (Change in Current) • Potential difference Constant current -> no potential diff Phy208 Lect. 25

  12. 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 Phy208 Lect. 25

  13. Inductors in circuits IL IL instantaneously zero, but increasing in time IL(t) Slope dI / dt = Vbattery / L 0 0 Time ( t ) Phy208 Lect. 25

  14. Just a little later… Switch closed at t=0 A short time later ( t=0+Δt ), the current is increasing … IL(t) • More slowly • More quickly • At the same rate IL>0, and IR=IL VR≠0, so VL smaller VL= -LdI/dt, so dI/dt smaller Slope dI / dt = Vbattery / L 0 0 Time ( t ) Phy208 Lect. 25

  15. λ Electromagnetic waves In empty space: sinusoidal wave propagating along x with velocity E = Emax cos (kx – ωt) B = Bmax cos (kx – ωt) • E and B are perpendicular oscillating vectors • The direction of propagation is • perpendicular to E and B Phy208 Lect. 25

  16. c B E Quick Quiz on EM waves z y x Phy208 Lect. 25

  17. Power and Intensity EM wave transports energy at its propagation speed. 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) Phy208 Lect. 25

  18. 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 Phy208 Lect. 25

  19. 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 Phy208 Lect. 25

  20. 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 Phy208 Lect. 25

  21. 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 Phy208 Lect. 25

  22. 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. Phy208 Lect. 25

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

  24. n=3 n=2 n=1 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 E31 > E21 so λ31 < λ21 Wavelength is smaller for larger jump! Phy208 Lect. 25

  25. 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. 1240 nm B. 413 nm C. 310 nm D. 248 nm E2=3 eV E1=1 eV Phy208 Lect. 25

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

  27. 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’sconstant Phy208 Lect. 25

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