Physics 202, Lecture 17
Today’s Topics
  Inductance (Ch 32)
  Reminder of Faraday’s and Lenz’s Laws
  Self Inductance
  Mutual Inductance
Review: Faraday’s Law of Induction
 Faraday’s Law in plain words: When the magnetic
flux through an area is changed, an emf is produced
along the closed path enclosing the area.
Quantitatively:
conventional
direction of ε
B
θ
  Energy Stored in B Field
  RL Circuits
A
Note the - sign
Review: Lenz’s Law
 Lenz’s law in plain words: the induced emf always
tends to work against the original cause of flux change
Cause of dΦB/dt
“Current” due to Induced ε will:
Increasing B
generate B in opposite dir.
Decreasing B
generate B in same dir.
Relative motion
subject to a force in opposite
direction of relative motions
Self Inductance
  When the current in a conducting device changes,
an induced emf is produced in the opposite direction
of the source current  self inductance
 The magnetic flux due to self
inductance is proportional to I:
 The induced emf is proportional
to dI/dt:
L: Inductance, unit: Henry (H)
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Exercise: Calculate Inductance of a Solenoid
 show that for an ideal solenoid:
Area: A
 For coupled coils:
ε2 = - M12 dI1/dt
ε1 = - M21 dI2/dt
2
L=
Mutual Inductance
µ0 N A
l
Can prove (not here):
M12=M21=M
(see board)
# of turns: N
€
Reminder: magnetic field inside the solenoid (Ch 30)
Examples of Coupled Coils (Transformers)
 M: mutual inductance
(unit: also Henry)
ε2 = - M dI1/dt
ε1 = - M dI2/dt
Energy Stored in a Magnetic Field
 When an inductor of inductance L is carrying a current
changing at a rate dI/dt, the power supplied is
 The work needed to increase the current in an inductor
from zero to some value I
!S
NS
=
!P
NP
U=
!
0
t
P dt =
!
0
I
LIdI =
1 2
LI
2
2
Energy in an Inductor
  Energy stored in an inductor is U= ½
LI2
Basic Circuit Components
Component
Symbol
Behavior in circuit
Ideal battery, emf
ΔV=V+-V- =ε
Resistor
Realistic Battery
 This energy is stored in the form of magnetic field:
energy density: uB = ½ B2/µ0 (recall: uE= ½ ε0E2)
 Compare:
Inductor: energy stored U= ½ LI2
Capacitor: energy stored U= ½ C(ΔV)2
Resistor: no energy stored, (all energy converted to heat)
RL Circuit
 An inductor and are resistance constitute a RL circuit
  Any inductor has a resistance, R
  R could also include any other additional resistance
 When the current starts to flow a voltage drop will
occur a the resistance and the inductance
 Once current stabilizes, reaches maximum of
ΔV= -IR
ε r

(Ideal) wire
Capacitor
Inductor
ΔV=0 (R=0, L=0, C=0)
ΔV=V- - V+ = - q/C, dq/dt =I
ΔV= - LdI/dt
(Ideal) Switch
Transformer
L=0, C=0, R=0 (on), R=∞ (off)
Future Topics
Diodes,
Transistors,…
Exercise: Turn on RL Circuit
Apply Kirchhoff loop rule
t
I=
−
V0
(1− e L / R )
R
€
3
Exercise: Turn on RL Circuit (cont)
t
I=
−
V0
(1− e L / R )
R
Exercise: Turn off RL Circuit
Apply Kirchhoff loop rule
€
I = I0e
Note: the time constant is τ=L/R
Quiz: What is the current when t=∞ ?
−
t
L /R
€
Exercise: Turn off RL Circuit (cont)
I = I 0e
−
t
L /R
€
Note: the time constant is τ=L/R
Quiz: What is the current when t=∞ ?
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