ElectromagnetismChapter 8

Summary of Important Equations to understand for the HW:

1. Vo No

--- = --- Vi Ni

2. v = c = λ · f

3. 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

Ni = 200turns

No = ?turns

• Vo/Vi = No/Ni

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

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.

In Class Exercise #2: What is the wavelength, λ, of an EM wave broadcast by

the radio station 95.5 FM?

velocity = c = λ * f

Known Unknown

f = 95.5MHz λ = ?m

c = 3 x 108m/s

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

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.jp

g

http://holly.mine.nu:8080/holly/irstatuenew.jpg

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?

λmax = 0.0029m-K/T

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

Differential Form (Optional) 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)