CONCEPTUAL MATERIAL FOR TEST THREE - Chapters 20-23
Chapter 20 - Electromagnetic Induction
Motional emf
- is a consequence of the Lorentz ("magnetic") force acting on
mobile charges (electrons in metals, for example) inside a
conductor moving in a magnetic field
- Lorentz force separates positive and negative charges inside the
conductor in effect creating a "battery"
- if a conducting loop is formed (recall metal rod sliding on
conducting rails) a current will flow
Magnetic flux
- informal view: "number of field lines passing through an area"
- for a uniform field passing through a flat area: the component of
the magnetic field perpendicular to the area times that area
Faraday's induction law
- more general than motional emf: applies to all induction situations
- states that an emf is induced around a closed loop in which the
magnetic flux is changing in time
- some common examples of Faraday's law at work
. permanent magnet entering or leaving a coil
. coil rotating in a magnetic field
. flexible coil changing shape in a magnetic field
. coil moving into or out of a region containing a magnetic field
. coil which contains a time-varying magnetic field
- the presence of the induced emf around a loop implies the existence
of an induced electric field around the loop
- the induced electric field is not electrostatic (electrostatic
fields cannot form closed loops)
- major applications of Faraday's laws: electric generators and the
common induction electric motor
Lenz' law
- is based on the conservation of energy
- determines direction of the induced emf around a loop: states that
the emf will be generated in a sense that will oppose the CHANGE
in the flux inside the loop
- direction of emf based on RHR:
. point thumb of right hand in direction of a magnetic field that
will oppose the CHANGE in the flux
. fingers curl in direction of the induced emf (or, equivalently,
of the induced electric field)
Self-induction
- results from Faraday's and Lenz' laws
. a time-varying current in a coil produces a time-varying magnetic
field (and hence a time-varying flux) in the coil;
. a changing flux induces an emf around a coil according to
Faraday's law
. the induced emf opposes the change of flux in a coil according to
Lenz' law
Inductance of a coil
- a measure of the strength of the self-induction of a coil
- depends soley on geometric properties ("how the coil is wound")
- is the constant of proportionality between the magnitude of the
induced emf in the coil and time rate of change of the current in
the coil
Self-inductance in practice
- try to increase current in coil: induced emf appears as a voltage
across the coil acting to oppose the increase in current
- try to decrease current in coil: induced emf appears as a voltage
across the coil acting to maintain the current
Energy in a magnetic field
- like the electric field, the magnetic field is viewed as containing
energy
- energy density of a magnetic field (energy per unit volume) at a
given point is proportional to the square of the field there
Electrical Safety (not in textbook)
- Three-prong plug
. hot wire: connected to small prong; switch should be on hot wire
. neutral wire: large prong
. ground wire: round prong; resistance from chassis of device to
ground should be as small as possible
- Short circuit
. where the current follows a path shorter than that intended
. can cause electrocution if the short is to an accessible part of
the device
. can also cause heating and even fire
. will at the least cause malfunction (may be critical or even
life-threatening in a hospital)
- Open circuit
. where the current can't flow due to a break in the circuit
. can cause malfunction (or failure)
. can cause electric shock if it results in exposure of an
electrified wire or component
- Fuse or circuit breaker
. purpose is to open the circuit if too much current is drawn
. bypassing this feature can lead to the hazards associated with a
short circuit
- Ground wire
. keeps the "chassis" of the electrical device at the same
potential as the ground
. prevents voltage drop across someone in contact with ground and
chassis
. if absent could allow a short circuit to the chassis to cause
electrocution
. by itself, may not prevent fire hazard (need both ground wire and
fuse)
- Ground Fault Circuit Interrupter (GFCI)
. important in areas where someone may come in contact with voltage
and have low resistance to ground (like kitchen or bathroom), since
currents too small to activate a fuse or circuit breaker can still
be dangerous
. makes an open circuit when a short to ground is detected
- Effects of electricity on body
. current is the danger, not just voltage (static electricity: high
voltage but very little current)
. muscles contract and lose the ability to respond to the brain
. low current: harmless to "can't let go" muscle contraction at
around 10-20 mA
. medium current: ventricular fibrulation at around 100-300 mA
and death if sustained; respiration continues
. high current: sustained ventricular contraction, respiratory
paralysis, burns at around 6 A and higher
- Use of high frequencies in medicine
. the higher the frequency, the less the penetration of the current
into a conducting substance (like flesh)
. current stays near surface of body
- Patient safety
. isolating patient electrically helps prevent patient becoming
part of a closed circuit
. monitoring wires, etc., that penetrate body can make a patient
"microshock sensitive" by bypassing high skin resistance
Chapter 21 - Alternating Current
Alternating current
- changes direction periodically instead of always flowing in same
direction
- has "sinusoidal" oscillation with time
- is produced by emf devices called "oscillators"
Time-varying voltage and current
- maximum voltage and current: voltage or current at either positive
or negative "peak" in the oscillation
- peak-to-peak: measured from negative to positive peak, = twice
maximum
- average voltage and current = 0 (equal positive and negative), hence
need for a measure of "effective" voltage and current
- effective (root mean square or rms) voltage and current = square
root of time average of the square of the voltage or current
- effective = maximum divided by square root of two
AC and resistance
- "Ohm's law" equations still applicable
- a resistance does not shift the voltage oscillation in time away
with respect to the current (voltage and current "in phase")
- average power = effective current times effective voltage
AC with capacitors or inductors
- both react to oppose the flow of AC
- this reactance is not dissipative as in the case for resistance
- reactance: the strength of opposition to the flow of current
- reactance is involved in "Ohm's law"-like equations (V = IX)
- reactance depends on the frequency of the AC
AC with capacitors
- capacitor is charged one direction, discharged, then charged in
the opposite direction, etc., as the current oscillates
- electrostatic repulsion of of charge in capacitor gives rise to
capacitive reactance
- capacitive reactance depends on 1/frequency and therefore
diminishes the higher the frequency
- reason for drop of reactance with f: the shorter the time of
charging the less charge can build up to oppose the current
- voltage oscillation across capacitor is shifted in time so that it
peaks 1/4 of a period after the current
- no power is dissipated by capacitive reactance
AC with inductors
- self-inductance opposes current flow
- inductive reactance increases with frequency
- increasing frequency -> more rapid change of magnetic flux in coil
-> increase in induced emf
- voltage oscillation across inductor is shifted in time so that it
peaks 1/4 period before the current
- no power is dissipated by inductive reactance
Remember "ELI the ICE man": ELI = voltage E leads current I in an
inductive (L) circuit; ICE = current leads voltage in a capacitive (C)
circuit.
Chapter 22 - Radiant Energy: Light
Electromagnetic (EM) waves are a consequence of Maxwell's equations
- Maxwell's equations:
. Gauss' law, closed magnetic loops, Ampere's law, Faraday's law
- EM waves result primarily from the coupling between electric and
magnetic fields contained in Ampere's and Faraday's laws
- Faraday's law: a time-varying magnetic field produces an
electric field
- Ampere's law needed "fixing"
. originally stated a current produces a magnetic field
. amended by Maxwell to show that a time-varying electric field
also produces a magnetic field
Properties of EM waves
- consist of vibrational disturbances in the electric and magnetic
fields that travel at the speed of light
- range from very long wavelength, low frequency radio waves to
short wavelength, high frequency gamma rays
- electromagnetic spectrum, from long to short wavelength
. radio, microwave, thermal infrared, near infrared, visible,
ultraviolet, xray, gamma ray
- in vacuum: consist of perpendicular electric and magnetic fields
propagating in a direction perpendicular to both fields (called
transverse electromagnetic waves or TEM waves)
- Frequency-wavelength relationship (same as for all periodic
waves): speed equals wavelength times frequency
- Frequency-wavelength relationship due to constant speed of light,
c: frequency increases as wavelength decreases
- irradiance (intensity) is the energy per unit area per unit time
of electromagnetic radiation
- irradiance is proportional to the square of the wave's electric
field amplitude
Classical origin of EM waves
- accelerating electrical charges radiate electromagnetic energy
- transmitting dipole antenna: emits electromagnetic radiation
through harmonic oscillation (an thus acceleration) of electrons
Quantum origin of EM waves
- EM waves consist of discrete bundles of energy called photons
- photon energy equals frequency of EM wave times Planck's constant
- quantum theory establishes energy levels for electrons in atoms,
molecules, solids, liquids, etc.
- "acceleration" of electrons accomplished by electrons jumping
from higher to lower energy levels in atoms, molecules, solids,
etc., and emitting a photon of EM radiation
- electrons can absorb photons by using the photon energy to bump
themselves up to a higher energy level or emit photons by
jumping to a lower energy level
Chapter 23: The Propagation of Light: Scattering
Scattering basics
- Quantum view of scattering: one photon is absorbed then another
emitted
- Elastic scattering: photon emitted has the same energy as the
photon absorbed
- Rayleigh scattering
. scattering by particles smaller than one wavelength
. shorter wavelengths are scattered more strongly than longer
ones (sky blue, sunset red)
- Interference
. superposition of two or more waves to form a resultant wave
. constructive: waves tend to reinforce each other (peaks coincide
with peaks, troughs with troughs)
. destructive: peaks and troughs tend to cancel each other
- Forward scattering
. forward moving waves are scattered constructively, allowing
propagation of EM waves through transparent media
Reflection
- occurs at the boundary between media with different indexes of
refraction
- external reflection: reflection off the surface with the higher
index of refraction
- internal reflection: reflection off the surface with the lower
index of refraction
- law of reflection: angle incident beam makes with normal to the
surface equals angle reflected beam makes with the normal ("angle
of incidence equals angle of reflection")
- specular reflection: all beams reflected parallel to each other
off a smooth surface
- diffuse reflection: reflection off rough surface
- flat mirror reflection: virtual image (not projectable on screen)
behind mirror same distance as object and right-left reversed
Refraction
- index of refraction (n) equals speed of light in vacuum divided by
speed of light in medium
- lower n to higher n: light bends toward the normal
- higher n to lower n: light bends away from normal
- frequency of light does not change from one medium to another
- wavelength of light gets shorter (longer) when going from lower
(higher) index of refraction to higher (lower)
- total internal reflection can occur if light in higher n medium
is incident of surface of lower n medium
- critcal angle: angle of incidence at which total internal
reflection first occurs