Electromagnetism Chapter 8

Summary of Important Equations to understand for the HW: 1. V o N o --- = --- V i N i 2.v = c = λ · f 3.λ max = / T

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

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

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

Transformers (more than meets the eye): n Steps up or down AC Voltages n Two coils close to each other n AC in the input coil induces an oscillating magnetic field through both coils n This changing magnetic field produces an AC current in the output coil n DC current would produce a steady magnetic field in the input coil and would not induce a current in the output coil n Each loop of the output coil has same induced voltage n Therefore, more loops (in output coil) == more output voltage (and vis versa) n Ratio of number of turns in the coils determines ratio of input and output voltages n V o N o --- = --- V i N i

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? KnownUnknown V i = 120V N i = 200turns N o = ?turns V o /V i = N o /N i V o = 600V

Electromagnetic Waves Introduction n 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.) n Transverse because both fields oscillate perpendicular to direction of propagation n Electric Field wave and Magnetic Field wave cannot exist separately n Travel at the speed of light (so-called because it was first measured for visible light), c = 3 x 10 8 m/s u c stands for celeritas, which is Latin for swift n 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 n 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 KnownUnknown f = 95.5MHz λ = ?m c = 3 x 10 8 m/s

BlackBody Radiation n Temperature affects amount and types of radiation emitted n Every object emits EM radiation because of the thermal motion of its atoms n 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 n The size and shape of the radiation curve changes with the object's temperature n The peak also changes with temperature: λ max = m-K / T

Mainly IR emitted… n All objects emit many types of radiation; the amount of each increases with temperature n 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)here n Sample IR photographs of objects emitting, or reflecting, IR radiation (courtesy of cam.com/): cam.com/   g g 

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?  λ max = m-K / T KnownUnknown T = 300K λ peak = ?m

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

Differential Form (Optional) n In differential form (see here and here for more):here  · E = ρ ⁄ ε o = 4πρ (in cgs)  · B = 0  × B = μ o ε o ∂E ⁄ ∂t + μ o J = 1 ⁄ c ∂E ⁄ ∂t + 4π ⁄ c J (in cgs)  × E = - ∂B ⁄ ∂t = - 1 ⁄ c ∂B ⁄ ∂t (in cgs)