Induced emf and magnetic flux

  emf - electromotive force

  flux - noun form of the word 'flow'

  Faraday's experiment - electric wire coiled around an iron ring.  Another
  coiled wire at the other end of the ring with a galvanometer attached to it.
  When the first circuit is turned on or off, it induced a change in the
  magnetic field, thus inducing a current in the other wire.

  An emf is produced in the second circuit by the changing magnetic field.

  Magnetic flux -

  Φ ≡ BA cosθ


Faraday's Law of Induction

  Experiment - a single coil of wire is attached to a galvanometer.  When a
  magnet is in motion through the loop, a current is induced.  The direction of
  motion determines the sign (+ or -) of the current.

  equation for emf:

  Ε = -N ΔΦ/Δt

  Where N is the number of coils, Φ is the magnetic flux; and t is time.

  Applications - guitar strings, SIDS devices



Motional EMF

  E=vB

  Where E is the Electric force, v is the velocity, and B is the strength of
  the magnetic field.

  ΔV = El = Blv

  The change in Voltage is equal to the Electric force times the length of the
  wire.

  Experiment : a free sliding bar is attached to two parallel and attached
  conductors.  The whole thing is within a magnetic field.  When the free
  sliding bar is moved, a current is produced.

  In this case:

  |Ε| =  ΔΦ/Δt = BlΔx/Δt = Blv

  Where Ε is the motional Emf, x is the distance that the bar is moved.

  If the resistance in that circuit is R, then the current is:

  I = Ε/R = Blv/R

Application of electromagnetic induction to the reproduction of sound

  guitar pickup - metallic, magnetizable string vibrates near a coil of wire,
  that moving magnetized string causes a change in the magnetic flux that passes
  through the coil, thus creating a current in the coil.

  tape recorder - the change in flux through the coil is due to the magnetized
  spots on the tape itself.

  microphone - sound waves cause a diaphram to move, which is connected to a
  coil of wire.  The moving coil of wire next to a stationary magnet produces
  a current due to the change in magnetic flux relative to the moving coil.


Lenz's Law

  The induced current must be in a direction such that the flux it produces
  opposes the change in magnetic flux.

  Consider the several different situations on p, 683 in light of this law.

Generators

  An AC generator in its simplest form consists of a rotating conductor
  inside a magnetic field.  That conductor is connected to rings, which
  rotate around another conductor.  The rotation within the magnetic field
  causes a change in flux, which induces a current in the wire.

  Ε = NBAω sin ωt

  Where ω is the angular speed.

  A DC generator is very similar, except that the rings are split.  This causes
  the current to move in only one direction.  However, it is pulsating, but
  always in the same direction.

Motors and back EMF

  A motor is a generator run in reverse.

  A current is applied to the loop which causes it to rotate because the of the
  fact that it is inside a magnetic field.

  As an application of Lenz's Law, there is back EMF generated by the motor.
  This is why it takes work to continue to turn a motor.


Mutual Inductance and Self-Inductance

  An Alternating current in one coil produces an electromagnetic field which
  induces an EMF arounf the coil, thereby creating a current in the second coil.

  M is the Mutual Inductance: units are Henrys (H)
  in reality, most values of M are very small, micro or mili

  M = NsΦs / Ip

  Ns is the number of coils is the secondary coil, Φs is the
  flux through one loop, I p is the current in the primary loop.

  EMF due to mutual inductance:

  EMFs = - M ΔIp/Δt

  In Self-Induction, the current is in the same coil.

  L is called the self-inductance or simple inductane of the coil.

  L = NΦ / I

  EMF due to self-induction

  EMF = -L ΔI/Δt

  Energy stored in an inductor

  ΔW = LI(ΔI)

  Energy = 1/2 LI2

  Energy density = Energy/Volume = I/2μ0 B2

  Energy can be stored in a magnetic field, just as it can be stored in an electric field.


The AC transformer

  To transform voltage or current, the current source is coiled around a
  conductive ring, the other end of the ring has another coil around it.  A
  current is induced in this second wire.

  ΔV2 = ΔV1 N2/N1

  Therefore:
  I1ΔV1 =I2ΔV2

  This assumes a perfect transformers.  Real transformers are between 90% and 99%
  efficient.

Maxwell's predictions

  Based on these known facts:

  1) Electric field lines originate at positive charges and end at negative
  charges
  2) Magnetic field lines formed closed loops
  3) Varying magnetic field induces an emf and hence an electric field.
  4) Magnetic field are generated by moving charges

  He predicted that electric and magnetic fields play symmetric roles in
  nature.

  He also proved that both electric and magnetic field travel at the speed of
  light in a vacuum, and that light itself is an electromagnetic wave.




HW 4:
p. 661 #1
p. 662 #10,20, etc... every multiple of 10 up to 70
8 problems total

due: 3/20/02

Have a good break!!!!!!!!