Resonance Curves of Multidimensional Chaotic Systems

1

• Last week
• A simple electric circuit consists of
• a current source, such as a car battery
• a resistor, such as a light bulb, or heater
• Voltage drop Resistance Current
• Power (Voltage drop) Current

A simple circuit A battery creates an voltage V
which pushes the current i through the resistor
R. In the wires, voltage and current are
constant. Units Current in Amperes A Voltage
in Volts V Resistance in Ohm O
2

• Magnets
• Context Magnetic fields make an electro-motor
  turn. A compass needle points to the North pole
  of the earth.
• Definition
• A magnet is a material or object that produces a
  magnetic field. A method to detect a magnetic
  field is to scatter iron filings and observe
  their pattern.
• Discussion
• Each magnet has a North and a South pole.
  Opposite poles attract each other, equal poles
  repel each other.
• A "hard" or "permanent" magnet is one that stays
  magnetized, such as the rock loadstone or iron
  (ferromagnet).
• A "soft" or "impermanent" magnet is one that
  loses its memory of previous magnetizations.
• A material without a permanent magnetic moment
  can, in the presence of magnetic fields, be
  attracted (paramagnetic aluminum), or repelled
  (diamagnetic graphite, super conductors).

Iron filings that have oriented in the magnetic
field produced by a bar magnet

• Lecture demos
• Load stone
• Bar magnet
• Broken magnet

3

• Electromagnets
• Context Electric current creates a magnetic
  field.
• Definition
• An electromagnet is a wire coil in which the
  magnetic field is produced by the flow of an
  electric current.
• Discussion
• When the current is off, there is no magnetic
  field. When the current changes, the magnetic
  field changes.
• An electromagnet creates a force and a torque on
  other magnets, including other electromagnets.
  This can be used to build electro motors.
• A changing magnetic field induces a current, and
  thus a magnetic field in a second coil (magnetic
  brakes).
• The direction of magnetic field in the second
  coil is opposite to the magnetic field in the
  first coil (repulsive force ? EM cannon).

Iron filings that have oriented in the magnetic
field produced by a coil carrying a current

• Lecture demos
• - Helmholtz coil
• EM cannon
• Faraday effect
• Motor 1, Motor 2
• magnetic brake

4

• Transformers
• Context High voltage power lines save energy.
• Definition
• A transformer are two coils that transfer
  electrical energy from one circuit to another
  through magnetic coupling. A changing current in
  the first coil (the primary ) creates a changing
  magnetic field in turn, this magnetic field
  induces a changing voltage in the second coil
  (the secondary).
• Discussion
• The secondary induced voltage V2 is scaled from
  the primary V1 by a factor ideally equal to the
  ratio of the number of turns of wire in their
  respective windings (N2, N1) V2/V1 N2/N1
• Power line energy loss resistance current2
• Energy transferred voltage current
• ? High voltage power lines are energy efficient

A transformer (2 coils) reduces The voltage from
10000V to 110V.

• Lecture demos
• Transformer
• EM cannon
• high voltage power line

5
Magnets transformers A magnet is a material or
object that produces a magnetic field. A method
to detect a magnetic field is to scatter iron
filings and observe their pattern. An
electromagnet is a wire coil in which the
magnetic field is produced by the flow of an
electric current. A transformer are two coils
that transfer electrical energy from one circuit
to another through magnetic coupling. A changing
current in the first coil (the primary ) creates
a changing magnetic field in turn, this magnetic
field induces a changing voltage in the second
coil (the secondary).
Iron filings that have oriented in the magnetic
field produced by a bar magnet a coil