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Lecture Notes for Chapters 8
- Reading Memo Insights:
- Summary of Important Equations to understand for the HW:
Vo No --- = --- Vi Ni
- v = c = λ · f
- λmax = 0.0029/T
- 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
- 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
- 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
- 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
- In-Class Exercise 1: 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?
Known Unknown Vi = 120V No = ?turns Ni = 200turns Vo = 600V
- 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
- What does the Electric Field look like? Pushed forward
and backward (increases then decreases)
- 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)
- v = c = 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.
- In-class Exercise 2: What is the wavelength,
λ, of an EM wave broadcast by the radio station 95.5
FM?
Known Unknown f = 95.5MHz λ = ?m c = 3 x 108m/s
- Imagine a charge is pushed forward and backward someplace
(oscillates)
- BlackBody Radiation (T 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
- 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/):
- In-class Exercise 3: Assuming that the human body is a
blackbody with a temperature of 310 K, at what wavelength,
λ, does it radiate the most energy?
Known Unknown T = 300K λpeak = ?m
- 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
- In differential form (see here and here for more):
∇ · E = ρ ⁄ εo = 4πρ (in cgs)
∇ · B = 0
∇ × B = μoεo ∂E ⁄ ∂t + μo J = 1⁄c ∂E ⁄ ∂t + 4π⁄c J (in cgs)
∇ × E = - ∂B ⁄ ∂t = - 1⁄c ∂B ⁄ ∂t (in cgs)
