Physics 54
Inductance and Oscillations
Everything is moving ahead on schedule, right over the cliff.
— Henry Kissinger
Magnetic energy and inductance
In the same way that a capacitor stores energy in the Efield, a device that creates a B
field when a current passes through it can store energy in the Bfield. Such a device is
usually called an
inductor
.
A solenoid provides a simple example. We consider a solenoid of crosssection area
A
and
n
turns per unit length carrying current
I
. We are interested in the work done as the
current builds up to its final value. This work represents the energy put into (and stored
in) the magnetic field of the solenoid.
At any instant, the magnetic flux through one turn of the solenoid is
Φ
m
=
BA
. The emf
induced in this turn is, by the flux rule,
E
1
=
−
A
⋅
dB
/
dt
. A length
d
of the solenoid
contains
nd
turns in series, which act like batteries in series, so their emf’s add. The total
emf induced in this length is
E
=
−
nAd
⋅
dB
/
dt
. Since the Bfield magnitude is given by
B
=
μ
0
nI
it follows that the total emf in length
d
of the solenoid is
E
=
−
μ
0
n
2
Ad
dI
dt
.
This formula shows that the emf is (minus) a geometric constant times the rate of
change of the current. The geometric constant is called the selfinductance:
Self inductance
The induced emf in an element due to a
changing current through the element is
given by
E
=
−
L
dI
dt
, where
L
is the self
inductance of the element.
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 Summer '09
 Thomas
 Physics, Current, Inductance, Energy, Magnetic Field, Inductor, Energy density, Faraday's law of induction

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