16.6) The Definition of Capacitance

  The capacitance, C, of a capacitor is defined as the ratio of the 
  magnitude of the charge on either conductor to the magnitude of the potential 
  difference between the conductors.
  
  C ≡ Q / ΔV
  
  Where Q is the charge in Coulombs, V is the voltage in volts, and C is the
  capacitance is farads (F).
  
16.7) The Parallel-Plate Capacitors

  C = εo A / d
  
  Where A is the area of one of the plates and d is the distance between the 
  plates.  εo is a constant:
  
  εo = 8.85 x 10-12 C2/N m2
  
  Symbols for elements, see p. 534.
  
16.8) Combinations of Capacitors

  Capacitors that are in parallel are equivalent to a single capacitor that 
  has a capacitance equal to the sum of the capacitors it replaces.
  
  for Parallel capacitors:  Ceq = C1 + C2 + C3 + ...
  
  
  Capacitors that are in series are more complicated.
  
  For series capacitors:
  
  1/Ceq = 1/C1 + 1/C2 + 1/C3...
  
16.9) Energy stored in a Charged Capacitor

  ΔW = ΔVΔQ
  
  Also, W = 1/2 QΔV
  
  Energy stored = 1/2 QΔV = 1/2 C(ΔV)2 = Q2/2C
 
 
MAGNETISM 
 
  
19.1) magnets

  magnets have poles, called North and South.
  
  As far as we know, it is impossible to have a single pole, poles must come
  in pairs, a North and a South.
  
  Like poles repel, opposites attract.
  
19.2) magnetic fields of the Earth

  The Earth has magnetic poles.  It turns out that the Earth's magnetic
  North pole is near the geographic South pole, and vice versa.  (pp.614)
  
  There is a distance of about 1200 miles between the magnetic poles and the
  geographic poles.
  
19.3) magnetic fields 
  
  F = qvB sin θ

  where F is the force, q is the charge, v is the velocity, B is the strength
  of the magnetic field, and θ is the angle between the v and the B.
  
  B is measured in Teslas (T).
  
  (p. 617)


  B ≡ F / qvsinθ
  
  Therefore, Fmax = qvB
  
  Right hand rule:
  
  Hold your right hand open.  If your thumb is in the direction of the velocity
  and your fingers point in the direction of the magnetic field, then the force
  is in the direction that your palm is pointing.
  
19.4) magnetic force on a current carrying conductor 

  p. 619
  
  if B is directed into the page, and the current is travelling up a wire,
  then the wire will bend to the left.
  
  for a current carrying conductor:
  
  F = BIl sin θ
  
  Where B is the strength of the magnetic field, I is the current, and l is the
  length of the wire, and θ is the angle between the current and the 
  magnetic field.
  
19.5) Torque on a Current Loop 

  τ = NBIA sin θ
  
  Where N is the number of turns in the coil, B is the strength of the magnetic
  field, I is the current, A is the area of the loop, θ is the angle
  between the middle of the loop and the electric field, and τ is the torque. 
  
  This is how an electric motor works.
  
  This is also how a galvanometer works, which is used in ammeters and volt 
  
  meters. 
  
19.6) The Galvanometer

  A galvanometer is a coiled wire with a current passing through it.  The coiled
  wire is allowed to rotate to an extent due to a spring.  When placed in a 
  magnetic field, the coil rotates.  The degree of rotation can be used to 
  measure the strength of the magnetic field.  If that magnetic field is caused
  by a current passing through another wire, you can determine the amount of
  current and the voltage.
  
  When a galvanometer is used as an Ammeter, it is placed in parallel with a
  resistor.
  
  When a galvanometer is used as a Voltmeter, it is placed in series with a
  resistor.
  
19.7) Motion of a charged particle in a magnetic field

  Using the right hand rule, a charged particle travelling perpendicular to a
  magnetic field will follow a circular pattern.
  
  r = mv/qB
  
  Where r is the radius, m is the mass, v is the velocity, q is the charge,
  and B is the magnetic field.
  
19.8) Magnetic Field of a long, straight wire and ampere's law.

  Right hand rule, put your thumb in the direction of the current, wrap your
  fingers around the wire.  The direction of your fingers determines the 
  direction of the magnetic field.
  
  Note, no distinct poles, the magnetic field continues in an infinite loop.
  
  B = μoI/2Πr
  
  Where B is the strength of the magnetic field, μo is a constant,
  the permeability of free space, I is the current, and r is the distance from
  the wire.
  
  μo ≡ 4 Π x 10-7T m/A
  
  
    
 19.9) Magnetic Force between Two Parallel Conductors.
 
   F1/l = μoI1I2 / 2 Πd  
   
   Where F is the force, l is the length of the length of a wire, μo
   is a constant, I is the current (in each wire), and d is the distance
   between the wires.
   
   
  
HW 12:
p. 640 CQ # 1,9   
p. 641 3 
p. 642 # 11
p. 643 # 19,25
p. 644 # 36
p. 645 # 42