Electrodynamics

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Electrodynamics
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• Suppose the force driving the charges is
  electromagnetic then
• J?EvB
• If purely electric
• J?E

Ohms Law Note, not a law, not always true
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Claim The field inside cyclinder is uniform

• Proof

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• Of all the stupid names this is perhaps the
  stupidest
• The emf is not a force it is not even a vector

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Faraday Again!
Faradays Law of Induction
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A simple generator In the shaded region there is
a uniform magnetic field pointing into the slide.
The resistor,R, whatever we want the current to
operate . Assume the entire loop is pulled
through the field with speed v, assume directly
to the right
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Emf is per unit charge
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• Notice that the integral to calculate E is
  performed at one instance in time

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Flux Rule(sometimes called Faradayss Law)

• The induced emf in a circuit is equal to the
  ngative rate at which the flux through the
  circuit is changing

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This rule applies to non-rectangular loops moving
in arbitary directions, through non uniform
magnetic fields
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Lenzs Law

• The induced current will be produced in such away
  as to oppose the change that produced it

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Faradays Law

• A changing magnetic field induces an electric
  field
• In the static case

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Inductance
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The mutual inductance

• M21is a purely geometric quantity depending only
  on the shapes and sizes of the two loops
• M21M12M
• Whatever the shapes and positions of the loops
  the flux through 2 when we run a current I around
  1
• is identical to the flux through 1 when we run a
  current I around 2

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Back emf

• Inductance like capacitance is an intrinsically
  positive quantity.
• Lenzs law dictates that the emf is in such a
  direction as to oppose any change in current.
• For this reason it is called a back emf

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Consequences

• Suppose there is a sudden break in a circuit
• I may be small but is enormous
• Generates a hugh emf sparks across break

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Energy in Magnetic fields
It takes a certain amount of energy to start a
current flowing in a circuit We need to
distinguish between the energy which is given off
as heat when the current passes through a
resistor this energy is irretrievably lost and
the work we must so against the back emf to get
the current going. This is recoverable. You get
it back when the current is turned off. It
represents energy latent in the circuit--- We can
regard it as energy stored in the magnetic field
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There is a problem!
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Note a)If we are dealing with Magnetostatics
Since ?.J0 E is constant in time b) Faradays
Law Says that a changing magnetic field induces
an electric field The Maxwell modified Amperes
Law Says that a changing electric field induces
an magnetic field c)
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Maxwells equations together with force
law FqEvxB Contains all of Classical
Electrodynamics
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S.da is the energy per unit time crossing an area
da
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Poyntings theorem The work done on the charges
by the electromagnetic forces is equal to the
decrease of energy stored in the fields the
energy that flowed out through the surface
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m/s
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m/s
Exactly the speed of light
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• An electric charge at rest sets up a pattern of
  electric field lines. A charge in motion sets up
  a pattern of magnetic field lines in addition to
  the electric field. Once a steady condition has
  been reached (after the charge is in motion and
  the fields are established in space)there is an
  energy density associated with the electric and
  magnetic fields but the energy density remains
  constant in time. However if you wiggle the
  charge back and forth you can send a signal.

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• Static charges and charges in motion at a
  constant rate do not radiate, accelerated charges
  radiate

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Consider the circuit shown . There is an energy
sourcethat restores the energy that is radiated
or lost as heat in the resistor. If the
resistance loses are small the current in the
circuit varies sinusodially with resonanceangular
frequency w( ?1/?LC ). The oscillator is coupled
through a transformer to a transmission line
which carries the current to an anteena, in this
case it is a simple dipole antenna
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