Electromagnetism

1. Electromagnetism Chapter 8

2. Summary of Important Equations to understand for the HW: • Vo No--- = --- Vi Ni • v = c = λ · f • λmax = 0.0029/T

3. Magnetism and The Magnetic Field • Understanding introduction to magnetism (10 mins) • Standard Deviants on Earth's magnetic field (10 mins) • Earth's geographic north precesses and magnetic north also moves around • Transparency 1: Fig. 8.6 on p. 280

4. Electricity and Magnetism • Moving electric charges (currents) produce magnetic fields (Right-Hand Rule) • Examples: solenoids, electrons in orbit around nucleus, protons and electrons spinning around, etc. • When electron domains align (say, with external H), ferromagnet becomes magnetic • Magnetic Field exerts force on a current carrying wire (that's perpendicular) • Electricity and Magnetism are both different manifestations of the same thing -- charge! • Magnetic fields used to trap plasmas and in particle accelerators • A moving magnet produces a circular electric field in the space around it • Coil of wire in motion will have current induced in it -- Electromagnetic Induction • This is the principle behind AC generators • Coil of wire is rotated in a magnetic field and produces an electric current

5. Electromagnetism • Changing Electric Field (or moving charges/current) induces a magnetic field • Changing Magnetic Field induces an electric Field • Changing can mean direction or strength

6. Transformers (more than meets the eye): • Steps up or down AC Voltages • Two coils close to each other • AC in the input coil induces an oscillating magnetic field through both coils • This changing magnetic field produces an AC current in the output coil • DC current would produce a steady magnetic field in the input coil and would not induce a current in the output coil • Each loop of the output coil has same induced voltage • Therefore, more loops (in output coil) == more output voltage (and vis versa) • Ratio of number of turns in the coils determines ratio of input and output voltages • Vo No--- = --- Vi Ni

7. A transformer is required to take a 120-V input voltage to a 600-V output voltage. If the input coil has 200 turns then how many turns should the output coil have? In Class Exercise #1: Vi = 120V No = ?turns Ni = 200turns Vo = 600V • Vo/Vi = No/Ni

8. Electromagnetic Waves Introduction • Imagine a charge is pushed forward and backward someplace (oscillates) • What does the Electric Field look like? Pushed forward and backward (increases then decreases) • Since we know E extends out to infinity, an oscillation increases then decreases this whole field (remember, field drops off in magnitude the farther out it is since E = F/Q) • But we know changing electric fields induce magnetic fields • But this induced magnetic field also increases and decreases (also oscillating since it's induced by the oscillating electric field) • And we know changing magnetic fields induce electric fields • Thus, an endless "loop" is established -- this combination of oscillating electric and magnetic fields is a transverse wave called an electromagnetic wave

9. EM Waves (contd.) • Transverse because both fields oscillate perpendicular to direction of propagation • Electric Field wave and Magnetic Field wave cannot exist separately • Travel at the speed of light (so-called because it was first measured for visible light), c = 3 x 108m/s • c stands for celeritas, which is Latin for swift • velocity = v = c = frequency * wavelength = f λ • Amplitude is the maximum value of the electric field and is proportional to the strength of the wave • Standard Deviants on Electromagnetism and light, spectra, etc.

10. What is the wavelength, λ, of an EM wave broadcast by the radio station 95.5 FM? velocity = c = λ * f In Class Exercise #2: λ = ?m f = 95.5MHz c = 3 x 108m/s

11. BlackBody Radiation • Temperature affects amount and types of radiation emitted • Every object emits EM radiation because of the thermal motion of its atoms • Blackbody: perfect absorber and emitter of radiant energy • For each Temperature, T, the distribution of radiant heat emission is characterized by a curve with a characteristic peak at a certain wavelength, λ • The size and shape of the radiation curve changes with the object's temperature • The peak also changes with temperature: λmax = 0.0029m-K/T

12. Mainly IR emitted… • All objects emit many types of radiation; the amount of each increases with temperature • IR can be emitted or reflected, just like all light, but IR light is the peak wavelength emitted by all objects with a Temp between about 9 K and 700 K (see here and problem 14) • Sample IR photographs of objects emitting, or reflecting, IR radiation (courtesy of http://www.holly-cam.com/): • http://holly.mine.nu:8080/holly/irfairyreaching.jpg • http://holly.mine.nu:8080/holly/iralmondchurchnew.jpg • http://holly.mine.nu:8080/holly/irstatuenew.jpg

13. Assuming that the human body is a blackbody with a temperature of 310 K, at what wavelength, λ, does it radiate the most energy? λmax = 0.0029m-K/T In Class Exercise #3: T = 300K λpeak = ?m

14. Maxwell's Equations in Integral Form (very optional) • Note: the integrals should be closed integrals • εo ∫ E • dS = q → says that charges (q) produce electric (E) fields • ∫ B • dS = 0 → says there are no such things as magnetic charges/monopoles • ∫ B • dl = μo (εo dΦE/dt + i) → says magnetic fields are produced both by currents (i) and by changing electric fields • ∫ E • dl = -dΦB/dt → says electric (E) fields are produced by changing magnetic fields

15. Differential Form (Optional) • In differential form (see here and here for more): • Ñ · E = ρ ⁄ εo = 4πρ (in cgs) • Ñ · B = 0 • Ñ × B = μoεo ∂E ⁄ ∂t + μoJ = 1⁄c ∂E ⁄ ∂t + 4π⁄cJ (in cgs) • Ñ × E = - ∂B ⁄ ∂t = - 1⁄c ∂B ⁄ ∂t (in cgs)