CONCEPTUAL MATERIAL FOR TEST TWO - Chapters 16-19
Chapter 16 - Electrostatics: Energy
- Electric potential energy
. arises because Coulomb force depends on position only and so is
a conservative force
. is the energy of electrical interaction between two or more charges
. equals the negative of the work done on a charge (or charges)
by the electrostatic field
. textbook: equals the the work done by the force or forces acting
against the electrostatic force (equivalent to above definition)
. can have an arbitrary zero level, usually taken to be the energy
where the charges are infinitely far apart
. for two charges is proportional to the product of the charges
divided by their separation (if zero PE is taken to be at
infinite separation of the charges)
- Electric potential
. defined at a point in space as the electrical PE a unit charge
would have if placed at that point (units of J/C = volts = V)
. is a scalar field
. like PE has an arbitrary zero level, usually taken to be at
infinity in electrostatics
. gives rise to expressing electric field in V/m (= N/C).
. superposition: the electric potential at a point is the scalar
sum of the potentials of all the charges in the vicinity
- Equipotential surfaces
. are imaginary surfaces along which the electric potential is
everywhere the same
. define the "shape" of the potential field
. are always perpendicular to electric field lines
. never touch or cross
- Potential due to a point charge
. proportional to the charge, falls off as 1/distance from charge
. equipotential surfaces of point charge are spherical surfaces
centered on the point charge
- Potential due to a uniform electric field
. rises (falls) steadily with change in position as you move
in the opposite (same) direction as the electric field lines
. equipotential surfaces are flat "sheets" perpendicular to the
electric field (parallel to the charge metal plates of a parallel-
plate capacitor, e.g.)
. equipotential surfaces close to a conducting surface are parallel
to that surface, meaning the electric field is nearly uniform
- Capacitance
. a measure of the amount of positive charge per volt that two
equally and oppositely charged objects can hold
. for oppositely charged conductors: depends only on geometry
. units = C/V = farads = F
- Parallel-plate capacitor
. capacitance proportional to area of plates and inversely
proportional to separation of plates
. contains a uniform electric field
- Capacitor combinations
. capacitors in parallel have same voltage across them but, in
general, contain different amounts of charge
. capacitors in series contain the same amount of charge but, in
general, have different voltages across them
- Energy in capacitors
. is electrical potential energy
. resides in the electric field
. is equal to 1/2 x charge x electric potential [(1/2)QV]
Chapter 17 - Direct Current
- Electric current
. flow of charge per unit time
. units of C/s = amps = A
- Emf
. produced by a device that converts energy into electric potential
energy by creating a charge separation
. battery: creates charge separation by chemical energy
. is defined as the potential measured across the device when no
current is flowing through the device
- Circuit
. a loop of electrical current
. must have a closed conducting loop
. contains direct current if direction of current in loop stays
the same
. drift "velocity": the mean speed of electrons in a circuit, on
the order of a mm or so per second
- Resistance
. defined as the voltage across a device divided by the current
. ohmic substances and devices: the resistance changes very
slightly with changes in the current
- Resistivity
. an "intensive" quantity - a property of a substance rather than
an object (like density versus mass)
. for current flow through a cylindrical shape = resitance x
cross-sectional area / length
. in ohmic substances, is largely due to collisions between
electrons and atomic vibrations (phonons)
. electron collisions with defects and impurities in the crystal
structure of a substance also contribute to resistivity (temper-
ature independent)
. increases slightly with temperature for ohmic substances due to
increase in vibration of atoms
. decreases slightly with temperature in semiconductors due to
addition of charge carriers (electrons or "holes")
. very high for insulators due to lack of charge carriers
. difference between conductors, semiconductors, insulators
.. conductors: no energy gap for electrons to hurdle to become
charge carriers (only highest energy electrons become charge
carriers due to Pauli exclusion principle
.. semiconductors: small energy gap that potential charge
carriers must hurdle
.. insulators: huge energy gap to hurdle
- Superconductiviy (not "high temperature")
. a state where there is no resistance to the flow of charge
. abruptly appears at a temperature called the critical temperature
(different for different substances) when the superconducting
substance is cooled
. results from a "phase change" when single electrons combine to
become Cooper pairs (one with "spin" up and the other spin down)
. Cooper pairs can carry charge without resistance because
.. they can move freely in the energy band (as bosons, they are
not subject to the Pauli exclusion principle)
.. they are not susceptible to scattering by the low-energy
phonons that exist at low temperatures because the phonons
only have enough energy to scatter them into the forbidden band
gap above the energy band, but Cooper pairs aren't allowed
there
- Electric power
. measured in watts (joules/second)
. = current x electric potential (= IV)
. energy from electric power often measured in kilowatt hours (kWh)
= energy from 1 kW working for one hour
Chapter 18 - Circuits
- Circuit principles
. circuit = closed conducting path containing emf(s) and resistance
. load resistance = resistance of device(s) that work in the
circuit (lights, motors, computers, etc.)
. terminal voltage = potential across battery as measured by ideal
voltmeter (infinite internal resistance)
. if no load on battery, terminal voltage = emf
. if load connected to battery, terminal voltage < emf
. branch = section of the circuit carrying a single current
. node = place where three or more branches connect
. loop = any closed current path
- Resistor networks
. series connection: resistors connected so that same current
flows through each resistor
. parallel connection: resistors connected so that the current
splits up into branch currents through each resistor
. series connection results in greater resistance than any single
resistor in the series
. parallel connection results in less resistance than any single
resistor in the connection
- Ammeter
. consists of a current-sensitive device (galvanometer) with a
very low "shunt" resistance connected in parallel
. shunt resistance: diverts vast majority of current from
galvanometer, allowing large currents to be measured by measuring
the small current that travels through the galvanometer
. connected in the circuit so that the current to be measured flows
through it
. the lower the resistance, the better the ammeter
- Voltmeter
. consists of galvanometer with a high series resistance
. high series resistance: handles by far most of the voltage drop
across the meter, allowing large voltages to be measured by
measuring the small current through the galvanometer
. connected across the device whose electric potential difference
is to be measured
. the higher the resistance, the better the voltmeter
Chapter 19 - Magnetism
Permanent magnets
- have at least two poles called "north" and "south"
- for a free-swinging magnet, the north pole points in the general
direction of the geomagnetic north pole (now in NE Canada)
- like poles repel, unlike attract
- are possible due to the "permanent magnetism" of ferromagnetic
materials
- isolated magnetic poles are not possible (except for possible
"magnetic monopole" elementary particle)
Magnetic field
- a vector field
- informal definition
. direction of the field at a given point in space equals
direction of the north pole of a "test compass" placed there
. magnitude of the field at a given point is proportional to the
torque experienced by the compass needle if it is rotated away
from alignment with the field
- magnetic field lines
. are only a picture and not real, like electric field lines
. show the direction of the magnetic field
. indicate a stronger field when closer together and a weaker
field when farther apart
Ferromagnetic materials
- derive their magnetism from the fact the electron acts like a
tiny magnet
- ferromagnetic elements: iron, nickel, cobalt
- atoms have a chemical shell (d shell) in which electrons align to
lower the atom's energy, enhancing the magnetism of the atom
- contain ferromagnetic "domains", regions where magnetic atoms are
aligned in the same direction
- when unmagnetized: the magnetic directions of the domains are
randomly distributed and not aligned
- when magnetized by an external magnetic field: the domains in
the direction of the field grow at the expense of the others
- domain alignment gives rise to strong magnetism of the ferro-
magnetic material when placed in an external magnetic field
Paramagnetic material
- weakly magnetic due to odd number of electrons per atom or
molecule
- odd electron gives atom or molecule a weak magnetism
- their electrons are (weakly) aligned by an external magnetic field
Diamagnetic material
- repelled by external magnetic fields
- develop a polarity oppose to that of the applied field
- due to orbiting electrons acting like current loops responding
to external field by opposing it
Earth's magnetism
- arises from electrical currents in liquid outer core
- looks like "bar magnet" to observers on and above earth's surface
- north geomagnetic pole is really a south pole and vice versa
Source of the magnetic field
- a moving electrical charge creates a magnetic field around it
- a stationary charge creates no field
- from a field point of view: a changing electric field (due to
the moving charge) creates (induces) a magnetic field
Electron magnetism
- classical explanation: electrons rotate and the moving charge
due to the rotation creates their magnetic field, turning them
into little magnets
- quantum explanation: electrons have "spin" (angular momentum)
and an intrinsic magnetism associated with this spin, but are not
rotating in any "common sense" fashion
Magnetism due to current flowing in straight wire
- field lines form circles around current flowing in a wire
- direction of field found from a right-hand rule: thumb of right
hand in direction of current, fingers curl in direction of field
- field strength falls off as 1/r from wire
Magnetism due to current flowing in loop
- loop acts like magnet with N and S poles
- N pole found by RHR: curl fingers of hand in direction of positive
current around loop, thumb points in direction of N pole
- coil: enhanced magnetism with multiple current loops by winding
a wire in various ways (solenoid, toroid, flat coil, etc.)
- solenoid: a coil where the turns form a long, straight cylinder
Ampere's law
- relates mathematically the magnetic field around a closed loop to
the net current flowing through the loop
- statement of, for circular field lines (as around a wire): the
strength of the field is proportional to the current flowing
through the loop and inversely proportional to the distance
around the loop
Lorentz ("magnetic") force
- force acting on a charged particle moving through a magnetic field
- is proportional to:
. the strength of the magnetic field
. the amount of charge on the particle
. the component of the particle's velocity that is perpendicular
to the field
- direction found from RHR: forefinger in direction of velocity,
middle finger in direction of prof, er, direction of magnetic
field, thumb gives direction of force
- cyclotron motion
. circular motion of a charged particle in uniform magnetic field
. due to Lorentz force acting as a centripetal force
. actual motion a spiral due to loss of energy
- Lorentz force is responsible for force on wires carrying current
in magnetic fields and torque on current loops in magnetic fields
Magnetic dipole moment
- a measure of the strength of the magnetism of a dipole magnet
such as loop or coil carrying current, bar magnet, electron, etc.