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NOTES
Faraday’s Law of Induction
The magnitude of the induced EMF in conducting loop is
equal to the rate at which the magnetic flux through the
surface spanned by the loop changes with time.

dΦ B

∫ Enc i ds = − dt where
N
Minus sign indicates the sense of EMF: Lenz’s Law
•  Decide on which way n goes
Fixes sign of ϕB
•  RHR determines the
positive direction for EMF
N
Ways to Change Magnetic Flux
•  Changing the magnitude of the field within a conducting loop (or coil).
•  Changing the area of the loop (or coil) that lies within the magnetic field.
•  Changing the relative orientation of the field and the loop.
motor
generator
http://www.wvic.com/how-gen-works.htm
Other Examples of Induction
+
-
Switch has been
open for some time:
Switch is just closed:
Nothing happening
EMF induced in Coil 2
+
-
Switch is just opened:
EMF is induced again
Switch is just closed:
EMF is induced in coil
-
+
Back emf
(counter emf)
MUTUAL
INDUCTANCE
BETWEEN
TWO COILS
©2008 by W.H. Freeman and Company
Eddy Currents
A current induced in a solid conducting
object, due to motion of the object in an
external magnetic field.
•  The presence of eddy current in the object
results in dissipation of electric energy
that is derived from mechanical motion
of the object.
•  The dissipation of electric energy in turn
causes the loss of mechanical energy of
the object, i.e., the presence of the field
damps motion of the object.
Self-Inductance
•  As current i through coil increases,
magnetic flux through itself increases.
This in turn induces counter
EMF in the coil itself
•  When current i is decreasing, EMF is
induced again in the coil itself in such a way
as to slow the decrease.
Self-induction
(if flux linked)
(henry)
Faraday’s Law:
NOTES
Inductance of a Solenoid: Basic Inductor Geometry
Current i flows through a long solenoid
of radius r with N turns in length l
For each turn
For the solenoid
or
Inductance, like capacitance, only depends on
geometry (if made of conductor and air)
Potential Difference Across Inductor
+V
ΔV
internal resistance
I
•  “Analogous” to a battery
•  An ideal inductor has r =0
V=0
•  All dissipative effects are to be
included in the internal resistance (i.e.,
those of the iron core if any)
Energy Stored By Inductor
1.  Switch on at t=0
As the current tries to begin flowing,
self-inductance induces back EMF, thus
opposing the increase of I.
+
2.  Loop Rule:
-
3. Multiply through by I
Rate at which energy is
stored in inductor L
Rate at which battery is
supplying energy
Rate at which energy is
dissipated by the resistor
NOTES
6C07
ENERGY STORED IN AN INDUCTOR
Where is the Energy Stored?
•  Energy must be stored in the magnetic field!
Energy stored by a capacitor is stored in its electric field
•  Consider a long solenoid where
area A
•  So energy density of
the magnetic field is
length l
(Energy density of the
electric field)
RL Circuits – Starting Current
1.  Switch to e at t=0
As the current tries to begin flowing,
self-inductance induces back EMF,
thus opposing the increase of I.
2.  Loop Rule:
3. Solve this differential equation
τ=L/R is the inductive
time constant
+
-
GROWTH AND DECAY OF CURRENT
OF AN RL CIRCUIT 6C-05
Starting and Decay Currents through an Inductor and a Capacitor
Remove Battery after Steady I already exists in RL Circuits
1.  Initially steady current Io is
flowing:
2.  Switch from e to f at t=0, causing
back EMF to oppose the change.
+
3.  Loop Rule:
4.  Solve this differential equation
I cannot instantly
become zero!
Self-induction
like discharging a capacitor
Behavior of Current through Inductors as Function of Time
•  Increasing Current
–  Initially, the inductor behaves like a battery connected in reverse.
–  After a long time, the inductor behaves like a conducting wire.
•  Decreasing Current
–  Initially, the inductor behaves like a reinforcement battery.
–  After a long time, the inductor behaves like a conducting wire.
Superconductor Repels External B field when T<TC
D
E
M
O
MAGNET LEVITATION ABOVE A SUPERCONDUCTOR
NOTES
Physics 241 Extra Quiz 3
The switch in this circuit is closed at t = 0.
What is the magnitude of the voltage across the
resistor a long time after the switch is closed?
(A) zero
(B)  V
(C)  R/L
(D) V/R
Physics 241 Extra Quiz 3
The switch in this circuit has been open for a
long time. Then the switch is closed at t = 0.
What is the magnitude of the current through the
resistor immediately after the switch is closed?
(A)  zero
(B)  V/L
(C) R/L
(D)  V/R
Warm up Quiz for AC
Which of the following statement is true?
A.
B.
C.
D.