Transcript ppt
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, 2009 Phy208 Lect. 25 1 Current loops & magnetic dipoles Current loop produces magnetic dipole field. Magnetic dipole moment: IA current Area of loop direction magnitude In a uniform magnetic field Magnetic field exerts torque B, B sin Torque rotates loop to align with B Tues. Dec. 1, 2009 Phy208 Lect. 25 2 Works for any shape planar loop r IA r perpendicular to loop I Torque in uniform magnetic field B, B sin r r Potential energy of rotation: U B Bcos Lowest energy aligned w/ magnetic field Highest energy perpendicular to magnetic field Tues. Dec. 1, 2009 Phy208 Lect. 25 3 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 4 Tues. Dec. 1, 2009 Phy208 Lect. 25 Magnetic flux • Magnetic flux is defined B dA B exactly as electric flux • (Component of B surface) x (Area element) Faraday’s law Time derivative d B dt EMF around loop Magnetic flux through surface bounded by path If path along conducting loop, induces current I=EMF/R Tues. Dec. 1, 2009 Phy208 Lect. 25 5 Quick quiz Which of these conducting loops will have currents flowing in them? A. C. I(t) increases Constant I B. Constant v Constant I Tues. Dec. 1, 2009 D. Constant v Constant I Phy208 Lect. 25 6 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, 2009 Phy208 Lect. 25 7 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. B=1T C. 1.5 1 0.5 0 0 0 -0.5 -1 0 45 90 135 180 225 270 315 360 -1.5 0 ANGLE ( DEGREES ) 45 90 135 180 225 270 315 360 ANGLE ( DEGREES ) 1.5 1.5 B. D. 1 1 0.5 0.5 0 0 0 0 -0.5 -0.5 -1 -1 -1.5 -1.5 0 45 90 135 180 225 270 315 360 ANGLE ( DEGREES ) Tues. Dec. 1, 2009 0 45 90 135 180 225 270 315 360 ANGLE ( DEGREES ) Phy208 Lect. 25 =0 in orientation shown 8 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, 2009 Phy208 Lect. 25 9 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. B. C. D. E. F. I Left Ftopside Iinduced Lloop Btop ILByˆ Right Up Down v Fbottomside Iinduced Lloop Bbottom ILByˆ Into page Out of page F F 0 cancel leftside Tues. Dec. 1, 2009 leftside Btop B bottom Force is up Phy208 Lect. 25 10 Inductors • Flux = (Inductance) X (Current) LI • Change in Flux = (Inductance) X (Change in Current) LI • Potential difference dI V L Constant current -> no potential diff dt Tues. Dec. 1, 2009 Phy208 Lect. 25 11 Energy stored in ideal inductor • Constant current (uniform charge motion) – No work required to move charge through inductor • Increasing current: – Work VLq VL Idt required to move charge across induced EMF dI – dW VL Idt L Idt LIdI dt – Total work W I 0 Tues. Dec. 1, 2009 1 2 Energy stored LIdI LI in inductor 2 Phy208 Lect. 25 12 Inductors in circuits IL t 0 0 VL t 0 Vbattery L dIL dt IL dIL Vbattery dt L IL instantaneously zero, but increasing in time IL(t) Slope dI / dt = Vbattery / L 0 0 Tues. Dec. 1, 2009 Time ( t ) Phy208 Lect. 25 13 Just a little later… Switch closed at t=0 IL(t) Slope dI / dt = Vbattery / L 0 0 Time ( t ) A short time later ( t=0+Δt ), the current is increasing … A. More slowly B. More quickly C. At the same rate Tues. Dec. 1, 2009 Phy208 Lect. 25 IL>0, and IR=IL VR≠0, so VL smaller VL= -LdI/dt, so dI/dt smaller 14 Electromagnetic waves In empty space: sinusoidal wave propagating along x with velocity E = Emax cos (kx – t) B = Bmax cos (kx – t) Bmax E /c • E and B are perpendicular oscillating vectors •The direction of propagation is perpendicular to E and B Tues. Dec. 1, 2009 Phy208 Lect. 25 15 Quick Quiz on EM waves z c E Tues. Dec. 1, 2009 Phy208 Lect. 25 x B y 16 Power and Intensity EM wave transports energy at its propagation speed. Intensity = Average power/area = 2 2 2 E max Bmax E max cBmax co E max I 2o 2oc 2o 2 Spherical wave: I Psource / 4 r 2 Radiation Pressure EM wave incident on surface exerts a radiation pressure prad (force/area) proportional to intensity I. Perfectly absorbing (black) surface: prad I /c Perfectly reflecting (mirror) surface: prad 2I /c Resulting force = (radiation pressure) x (area) Tues. Dec. 1, 2009 Phy208 Lect. 25 17 Polarization Linear polarization: Linear polarizer: E-field oscillates in fixed plane of polarization Transmits component of E-field parallel to max max E before cos transmission axis E after Absorbs component perpendicular to transmission axis. 2 Intensity I E max Iafter Ibefore cos2 Circular Polarization E-field rotates at constant magnitude Tues. Dec. 1, 2009 Phy208 Lect. 25 18 Quantum Mechanics • Light comes in discrete units: – Photon energy E photon hf hc / 1240 eV nm / • Demonstrated by Photoelectric Effect – Photon of energy hf collides with electron in metal – Transferssome or all of hf to electron – If hf > (= workfunction) electron escapes Electron ejected only if hf > min Minimum photon energy E photon hf required Tues. Dec. 1, 2009 Phy208 Lect. 25 19 Photon properties of light • Photon of frequency f has energy hf – E photon hf hc / – h 6.626 1034 J s 4.14 1015 eV s – hc 1240eV nm • 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, 2009 Phy208 Lect. 25 20 Photon energy What is the energy of a photon of red light (=635 nm)? A. 0.5 eV B. 1.0 eV 1240 eV nm E 1.95 eV 635 nm hc C. 2.0 eV D. 3.0 eV Tues. Dec. 1, 2009 Phy208 Lect. 25 21 Bohr’s model of Hydrogen atom Planetary model: Circular orbits of electrons around proton. Quantization 2 r n ao Discrete orbit radii allowed: n 2 Discrete electron energies: E n 13.6 /n eV Each quantum state labeled by quantum # n How did he get this? Quantization of circular orbit angular mom. L r p mvr n Tues. Dec. 1, 2009 Phy208 Lect. 25 22 Consequences of Bohr model • Electron can make transitions between quantum states. • Atom loses energy: photon emitted E photon E atomninitial E atomn final • Photon absorbed: atom gains energy: E photon E atomn final E atomninitial E atom n Tues. Dec. 1, 2009 Phy208 Lect. 25 13.6eV n2 23 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. 31 < 21 n=3 n=2 B. 31 = 21 C. 31 > 21 E31 > E21 so E hf hc 31 < 21 Wavelength is smaller for larger jump! Tues. Dec. 1, 2009 Phy208 Lect. 25 n=1 24 Question This quantum system (not a hydrogen atom) has energy levels as shown. Which photon could possibly be absorbed by this system? A. 1240 nm B. 413 nm E photon hc 1240 eV nm E3=7 eV E3=5 eV E2=3 eV C. 310 nm E1=1 eV D. 248 nm Tues. Dec. 1, 2009 Phy208 Lect. 25 25 Matter Waves • deBroglie postulated that matter has wavelike properties. • deBroglie wavelength h / p Example: Wavelength of electron with 10 eV of energy: Kinetic energy p2 E KE p 2mE KE 2m h hc 1240eV nm 0.39nm 2 6 2mE KE 2mc E KE 20.51110 eV 10eV Tues. Dec. 1, 2009 Phy208 Lect. 25 26 Heisenberg Uncertainty Principle Using x = position uncertainty p = momentum uncertainty Planck’s constant Heisenberg showed that the product ( x ) ( p ) is always greater than ( h / 4 ) Often write this as x p ~ /2 h is pronounced ‘h-bar’ 2 where Tues. Dec. 1, 2009 Phy208 Lect. 25 27