.m files

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time-varying magnetic fields equation of
continuity
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Faraday 1791-1867
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An induced electric current flows in a direction
such that the current opposes the change that
induced it. This law was deduced in 1834 by the
Russian physicist Heinrich Friedrich Emil Lenz
(1804-65).
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Faradays law
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a
a
magnetic field changes in time
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size of loop changes in time
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L
w
R
j
size of loop changes in time
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Faradays law
apply Stokes theorem
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This is a big one!
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This is a big one!
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wire carrying current I
nonuniform B field
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Bewleys book

• trick questions
• not every motion generates a voltage
• uniform B v
• substitution of circuit
• Vgen 0!

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X
B
V12 0
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X
B
u
c
1 2
V12 Bcu
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X
B
u
c
1 2
V12 Bcu
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X
B
V12 Bcu
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X
B
u
c
1 2
V12 Bcu
V12 -Bcu
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X
B
u
c
1 2
V12 Bcu
V12 -Bcu
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electromagnetic launcher
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J. Phys. D 33, 120 (2000)
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before
after
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Iowa State gun
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Equation of continuity

• economics
• If more comes out than you put in, the bag will
  decrease!
• There will be a flux of .
• Flux is related to what is or was inside the bag.

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• note that there is a flux out through a surface
  Dz Dy _at_ a time t gt 0
• flux density Ds - ? ( density)/?t Dv
• evaluate _at_ xo

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Gauss's theorem
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equation of continuity
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example place some charges on a conductor. How
long does it take for the charges to spread out?
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metal has a conductivity
Ohm's law
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Poisson's equation
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Poisson's equation
solution
time constant
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U. S. Congress has a source.
Gutenberg
What Congress brings home?
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