Tue. Nov. 9, 2009Physics 208, Lecture 201 From last time… Inductors in circuits Inductors Flux = (Inductance) X (Current)

V batt R L I VbVb VaVa Voltage drop across inductor Constant current No voltage difference Current changing in time Voltage difference across inductor Tue. Nov. 9, 2009Physics 208, Lecture 202

RL Circuit What is voltage across L just after switch closed? Tue. Nov. 9, 2009Physics 208, Lecture 203 Before switch closed, I L = 0 Current through inductor cannot ‘jump’ Just after switch closed, I L = 0. A.V L = 0 B.V L = V battery C.V L = V battery / R D.V L = V battery / L Kirchoff’s loop law: V R + V L = V battery R and L in series, I L =0  I R =0, V R =0

Tue. Nov. 9, 2009Physics 208, Lecture 204 ILIL IL(t)IL(t) Time ( t ) 0 0 Slope dI / dt = V battery / L I L instantaneously zero, but increasing in time

Just a little later… A short time later ( t=0+Δt ), the current is increasing … Tue. Nov. 9, 2009Physics 208, Lecture 205 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

Tue. Nov. 9, 2009Physics 208, Lecture 206 ILIL IL(t)IL(t) Time ( t ) 0 0 Initial slope What is current through inductor in equilibrium, a long time after switch is closed? Later slope A.Zero B.V battery / L C.V battery / R Equilibrium: currents not changing dI L / dt =0, so V L =0 V R =V battery I L = I R =V battery / R

Tue. Nov. 9, 2009Physics 208, Lecture 207 RL summary I(t) = time constant I(t)I(t) Switch closed at t=0

Question What is the current through R 1 immediately after the switch is closed? Tue. Nov. 9, 2009Physics 208, Lecture 208 L R1R1 R2R2 A.V battery / L B.V battery / R 1 C.V battery / R 2 D.V battery / (R 1 +R 2 ) E.0 I L cannot ‘jump’. I L =0 just after closing switch. All current flows through resistors. Resistor current can jump.

Thinking about electromagnetism Many similarities between electricity, magnetism Some symmetries, particularly in time-dependence Tue. Nov. 9, 2009Physics 208, Lecture 209 Electric Fields Arise from chargesCapacitor, Q=CV Arise from time-varying B-fieldInductor, Faraday effect Magnetic Fields Arise from currentsInductor, Φ=LI Arise from time-varying E-field

Tue. Nov. 9, 2009Physics 208, Lecture 2010 Maxwell’s unification Intimate connection between electricity and magnetism Time-varying magnetic field induces an electric field (Faraday’s Law) Time-varying electric field generates a magnetic field This is the basis of Maxwell’s unification of electricity and magnetism into Electromagnetism In vacuum:

Tue. Nov. 9, 2009Physics 208, Lecture 2011 A Transverse wave. Electric/magnetic fields perpendicular to propagation direction Can travel in empty space f = v/, v = c = 3 x 10 8 m/s (186,000 miles/second)

Tue. Nov. 9, 2009Physics 208, Lecture 2012 The EM Spectrum Types are distinguished by frequency or wavelength Visible light is a small portion of the spectrum

Tue. Nov. 9, 2009Physics 208, Lecture 2013 Sizes of EM waves Visible light typical wavelength of 500 nm = = 0.5 x m = 0.5 microns (µm) AM 1310, your badger radio network, has a vibration frequency of 1310 KHz = 1.31x10 6 Hz What is its wavelength? A.230 m B m C.2.3 m D.44m

Tue. Nov. 9, 2009Physics 208, Lecture 2014 A microwave oven irradiates food with electromagnetic radiation that has a frequency of about Hz. The wavelengths of these microwaves are on the order of A. kilometers B. meters C. centimeters D. micrometers Quick Quiz

Tue. Nov. 9, 2009Physics 208, Lecture 2015 Mathematical description z x y Propagation direction =

Tue. Nov. 9, 2009Physics 208, Lecture 2016 EM Waves from an Antenna Two rods are connected to an ac source, charges oscillate between the rods (a) As oscillations continue, the rods become less charged, the field near the charges decreases and the field produced at t = 0 moves away from the rod (b) The charges and field reverse (c) The oscillations continue (d)

Tue. Nov. 9, 2009Physics 208, Lecture 2017 Detecting EM waves FM antennaAM antenna Oriented vertically for radio waves

Tue. Nov. 9, 2009Physics 208, Lecture 2018 Transatlantic signals Gulgielmo Marconi’s transatlantic transmitter Capacitor banks Induction coils Spark gap

Tue. Nov. 9, 2009Physics 208, Lecture 2019 Transatlantic receiver Left to right: Kemp, Marconi, and Paget pose in front of a kite that was used to keep aloft the receiving aerial wire used in the transatlantic radio experiment.

Tue. Nov. 9, 2009Physics 208, Lecture 2020 Energy and EM Waves Energy density in E-field Energy density in B-field Total moves w/ EM wave at speed c

Tue. Nov. 9, 2009Physics 208, Lecture 2021 Power and intensity in EM waves Energy density u E moves at c Instantaneous energy flow = energy per second passing plane = This is power density W/m 2 Oscillates in time Time average of this is Intensity =

Tue. Nov. 9, 2009Physics 208, Lecture 2022 Example: E-field in laser pointer 3 mW laser pointer. Beam diameter at board ~ 2mm Intensity = How big is max E-field?

Tue. Nov. 9, 2009Physics 208, Lecture 2023 Spherical waves Sources often radiate EM wave in all directions Light bulb The sun Radio/tv transmission tower Spherical wave, looks like plane wave far away Intensity decreases with distance Power spread over larger area Source power Spread over this surface area

Tue. Nov. 9, 2009Physics 208, Lecture 2024 Question A radio station transmits 50kW of power from its antanna. What is the amplitude of the electric field at your radio, 1km away. A.0.1 V/m B.0.5 V/m C.1 V/m D.1.7 V/m E.15 V/m

Tue. Nov. 9, 2009Physics 208, Lecture 2025 The Poynting Vector Rate at which energy flows through a unit area perpendicular to direction of wave propagation Instantaneous power per unit area (J/s. m 2 = W/m 2 ) is also Its direction is the direction of propagation of the EM wave This is time dependent Its magnitude varies in time Its magnitude reaches a maximum at the same instant as E and B

Tue. Nov. 9, 2009Physics 208, Lecture 2026 Radiation Pressure Saw EM waves carry energy They also have momentum When object absorbs energy U from EM wave: Momentum  p is transferred Result is a force Pressure = Force/Area = ( Will see this later in QM ) Radiation pressure on perfectly absorbing object Power Intensity

Tue. Nov. 9, 2009Physics 208, Lecture 2027 Radiation pressure & force 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)

Tue. Nov. 9, 2009Physics 208, Lecture 2028 Question A perfectly reflecting square solar sail is 107m X 107m. It has a mass of 100kg. It starts from rest near the Earth’s orbit, where the sun’s EM radiation has an intensity of 1300 W/m 2. How fast is it moving after 1 hour? A.100 m/s B.56 m/s C.17 m/s D.3.6 m/s E.0.7 m/s