Review: Faraday’s Law of Induction
Physics 202, Lecture 17
 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
Today’s Topics

Inductance
 Reminder of Faraday’s and Lenz’s Laws
 Self Inductance
 Mutual Inductance
ε = − dΦ B
dt

Energy Stored in B Field


RL Circuits
Reminder: Midterm 2, Nov 2, 5:30-7PM (email for details)
Note the - sign
Review: Lenz’s Law
Increasing B
A
Φ B = ∫ B • dA
Self Inductance
 Lenz’s law in plain words: the induced emf always
tends to work against the original cause of flux change
Cause of dΦB/dt
θ
“Current” due to Induced
ε will:
 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:
generate B in opposite dir.
Decreasing B
generate B in same dir.
Relative motion
subject to a force in opposite
direction of relative motions
The induced emf is proportional
to dI/dt:
L: Inductance, unit: Henry (H)
Exercise: Calculate Inductance of a Solenoid
 show that for an ideal solenoid:
Area: A
Mutual Inductance
 For coupled coils:
ε2 = - M12 dI1/dt
ε1 = - M21 dI2/dt
µ N 2A
L= 0
l
Can prove (not here):
M12=M21 =M
(see board)
# of turns: N
Reminder: magnetic field inside the solenoid (Ch 27)
 M: mutual inductance
(unit: also Henry)
ε2 = - M dI1/dt
ε1 = - M dI2/dt
Examples of Coupled Coils (Transformers)
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
Energy in an Inductor
 Energy stored in an inductor is U= 1/2 LI2
Basic Circuit Components
Component
Symbol
Behavior in circuit
ΔV=V +-V- = ε
Ideal battery, emf
ΔV= -IR
ε r
Resistor
Realistic Battery
 This energy is stored in the form of magnetic field: energy density:
uB = 1/2 B 2/µ0 (recall: uE= 1/2 ε0E 2)
 Compare:
Inductor: energy stored U= 1/2 LI2
Capacitor: energy stored U= 1/2 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 at the resistor and the inductor.
 Once current stabilizes, reaches maximum of

(Ideal) wire
ΔV=0 (R=0, L=0, C=0)
Capacitor
ΔV=V - - V + = - q/C, dq/dt =I
Inductor
ΔV= - LdI/dt
(Ideal) Switch
L=0, C=0, R=0 (on), R=∞ (off)
Transformer
Diodes,
Transistors,…
Future Topics
Exercise: Turn on RL Circuit
Apply Kirchhoff loop rule
I=
t
−
V0
(1− e L / R )
R
Exercise: Turn on RL Circuit (cont)
I=
V0
(1− e
R
t
−
L /R
)
Note: the time constant is τ=L/R
Quiz: What is the current when t=∞ ?
Exercise: Turn off RL Circuit (cont)
I = I0e
−
t
L /R
Note: the time constant is τ=L/R
Quiz: What is the current when t=∞ ?
Exercise: Turn off RL Circuit
Apply Kirchhoff loop rule
I = I0e
−
t
L /R