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 - PowerPoint PPT Presentation
Transcript of time-varying magnetic fields equation of continuity
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).
Faraday’s law dt
tdtV m
ΔsB tΨm
s
dt
tdILtV
zudxdyds
T
BeatV
Tt
2
tTBe
B zu
dt
dtV m
dt
BeadtV
Tt
2
x y
z
dsBm
dsBm
zudxdyds
zuB B
dt
dtV m
dt
tsinABdtV
x y
z
tsinAAs
tcosABtV
x y
z dsBm
dt
dtV m
cosBLWm
dt
d
d
dtV m
tsinBLWtV R
tVtI
dlE
t
dsBdlE
t
dsBdsEdlE
dsEdlE x
Faraday’s law
apply Stoke’s theorem
t
dsB
tx
B
E
tx
dsBdsEdlE
t
x
B
E 0 t
x
B
E 0
0x E
0 B
t
B
tx
B
E
I eat allmagnetic
monopoles!
wire carrying current I
Luwx2
IV o
I
2w
Lu
V
22o
wx
ILwuV
x
Luwx2
Io
Bewley’s book
trick questions not every motion
generates a voltage uniform B & v substitution of circuit Vgen = 0!
XB
XB
1 2
cu
V12= 0
XB
1 2
cu
V12= Bcu
XB
1 2
cu
V12= Bcu
XB
V12= Bcu1 2
cu
XB
1 2
cu
V12= -Bcu
V12= Bcu
XB
1 2
cu
V12= -Bcu
V12= Bcu
1
I1 dl1
B2
I2 dl2
B1
BvdF dQ
dvv BvdF dsdlBjdF
BIdldF
Equation of continuity economics If more comes out
than you put in, the bag will decrease!
There will be a flux of $.
Flux is related to what is or was inside the bag.
note that there is a flux out through a surface z • y @ a time t > 0
[flux density] • s = - [ ($ density)/t] • v evaluate @ xo