1
Physics 1C
Week 3 notes©
W. Gekelman
Faraday’s Law
!
=
"
#$
B
#
t
leads us to the concept of inductance.
If one part of a circuit
produces
a changing magnetic flux and this in turn goes through a loop in another part of
a circuit or in an adjacent circuit it will induce a voltage and perhaps a current there.
In this case the solenoid has a changing current which means there is a changing flux in the
3 loop circuit wrapped around it. The magnetic B is always directly proportional to the
current (this is true in Amps law or the Law of Biot and Savart) If B is proportional to
the current, i, so is the flux
!
B
and therefore so is the EMF
!
=
"
#$
B
#
t
=
"
stuff
(
)
di
dt
. Let us define this stuff to be L, the inductance.
Therefore
!
=
"
#$
B
#
t
=
"
L
di
dt
.
The inductance depends only upon the geometry.
Consider two circuits one next to another
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2
A changing current in coil 1 will induce a changing current in coil 2
!
2
=
"
N
2
d
#
21
dt
.
N
2
is the number of turns in coil2 and
!
21
is the flux in coil 2 because of
the changing currents in coil 1.
Since the flux is proportional to the inductance:
!
2
=
"
M
21
di
1
dt
.
This is the EMF in 2 because of the changing currents in 1.
M
21
is called
the mutual inductance in 2 due to 1.
This works both ways:
!
1
=
"
M
12
di
2
dt
.
This isn’t
everything! Consider a solendoil with a changing current in it.
If the solenoid has N turns
then the first N1 turns produce a changing flux on the last turn, which causes a counter or
back EMF on it.
The changing flux when you sum this up will have a total EMF that
opposes the changing current and will be in the opposite direction as the original EMF (or
Volatge) the drove the current.
The inductance of a coil due to itself is called the self
inductance, L, and is given by:
(1)
!
=
"
N
d
#
B
dt
=
"
L
di
dt
L
=
N
#
B
i
i is the instantaneous current in the coil and
Φ
B
is the flux
through the coil due to its own current.
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 Winter '07
 Whitten
 Inductance, dt, DI

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