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time-varying magnetic fields equation of continuity. Faraday 1791-1867. 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). either B or
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time-varying magnetic fields equation of continuity
Faraday 1791-1867
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).
either B or change in time or both change in time Faraday’s law
z B ds y x a a magnetic field changes in time
z B ds y x size of loop changes in time
z B y x L R w j size of loop changes in time
Faraday’s law apply Stoke’s theorem
I eat all magnetic monopoles! This is a big one!
2w L u I x DV wire carrying current I nonuniform B field
Bewley’s book • trick questions • not every motion generates a voltage • uniform B & v • substitution of circuit • Vgen = 0!
X B u c 1 2
u c 1 2 X B V12= 0
X B u c 1 2 V12= Bcu
X B u c 1 2 V12= Bcu
u c 1 2 X B V12= Bcu
X B u c 1 2 V12= Bcu V12= -Bcu
X B u c 1 2 V12= Bcu V12= -Bcu
I1 dl1 I2 dl2 1 B2 B1
electromagnetic launcher
before after
Equation of continuity • economics • If more comes out than you put in, the bag will decrease! • There will be a flux of $. • Flux is related to what is or was inside the bag.
note that there is a flux out through a surface Dz • Dy @ a time t > 0 • [flux density] • Ds = - [ ($ density)/t] • Dv • evaluate @ xo
example: place some charges on a conductor. How long does it take for the charges to spread out?
metal has a conductivity Ohm's law
Poisson's equation solution time constant
U. S. Congress has a source. Gutenberg What Congress brings home?