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LECTURE 23
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Start chapter 31: read 31.1-31.3
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Inductance
Mutual inductance
 2 M 2,1I1
dI1
E2   M 2,1
dt
Self- inductance
 1 L I1
dI1
E1   L
dt
Exercise: Calculate the mutual inductance M
and self-inductance L for both solenoids in the
picture shown below.
I2
l2
r2
r1
l1
Hint: the magnetic field
inside a solenoid is
N
B  0 I
l
Exercise: Label points A and B with plus
or minus signs, according to the polarity
of the self-induced emf.
Concept test: A coil with self-inductance L
carries a current I given by I = I0 sin(wt). The
graph that describes the self-induced emf as a
function of time is
1.)
2.)
3.)
4.)
5.)
Magnetic energy
dU B
dI
P
 I ( Emf )  LI
dt
dt
Magnetic field
energy
Electric field
energy
1 2
U B  LI
2
1
U E  CV 2
2
Magnetic energy density
1
uB 
B2
2 0
Magnetic field
Energy density
1
uE   0 E 2
2
Electric field
Energy density
Application: The coaxial cable
(a) Use Ampere’s law to calculate B(r)
(b) Calculate the self-inductance L of the
cable, per unit length
Application: The coaxial cable (cont’d)
(c) How much energy is stored/unit length?
(d) Where is the energy density highest?