1. 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.
where N
Minus sign indicates the sense of EMF: Lenz’s Law
Decide on which way n goes
Fixes sign of ΦB N
RHR determines the positive direction for EMF 

2. Motional EMF of Sliding Conductor
Induced EMF:
Lenz’s Law gives direction
counter-clockwise
Faraday’s Law
FM decelerates the bar
This EMF induces current I
Magnetic force FM acts on this I

3. 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.
generator
motor

4. Other Examples of Induction
EMF induced in Coil 2 + -
EMF is induced again + -
Switch has been open for some time:
Nothing happening
Switch is just opened:
Switch is just closed:
EMF is induced in coil + -
Switch is just closed:
Back emf (counter emf)

5. Eddy Current
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.

6. Reading Quiz 1 Which of the following statements is incorrect?
A| The inductance of a coil with N turns is proportional to N2 turns.
B| Like a capacitance (C) an inductor (L) depends on geometric factors and the nature of the material inside C and L.
C| The potential across an inductor depends only on the magnitude
of the current through the inductor.
D| The magnetic energy stored in an inductor is proportional to the
square of the current through the inductor.

7. Self-Inductance Self-induction (henry) Faraday’s Law:
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:

8. DOCCAM 2

9. Inductance and Faraday’s Law
(henry) + -
compare with

10. Solenoid: Archetypical Inductor
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)

11. Potential Difference Across InductorΔV +V
V=0 I
internal resistance
“Analogous” to a battery
An ideal inductor has r =0
All dissipative effects are to be included in the internal resistance (i.e., those of the iron core if any)

12. Warm-up quiz 1
The circuit is turned on at t=0. Which of the following statement is correct? R1 R2 L V
A| At t = 0, the potential drop across the inductor is V; When t = ∞, the current through R1 is V/R1
B| At t = 0, the potential drop across the inductor is 0; When t = ∞, the current through R1 is V.
C| At t = 0, the potential drop across the inductor is V; When t = ∞, the current through R1 is V/(R1+R2)
D| At t = 0, the potential drop across the inductor is V; When t = ∞, the current through R1 is V/R2

13. Energy Stored By Inductor
Switch on at t=0
As the current tries to begin flowing, self-inductance induces back EMF, thus opposing the increase of I. + -
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

14. DOCCAM 2

15. 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
length l
So energy density of the magnetic field is
(Energy density of the electric field)

16. RL Circuits – Starting Current
Switch to e at t=0
As the current tries to begin flowing, self-inductance induces back EMF, thus opposing the increase of I. + -
Loop Rule:
3. Solve this differential equation
τ=L/R is the inductive
time constant

17. DOCCAM 2

18. Starting Current through Inductor vs Charging Capacitor

19. Remove Battery after Steady I already exists in RL Circuits
Initially steady current Io is flowing: - +
Switch from e to f at t=0, causing back EMF to oppose the change.
Loop Rule:
Solve this differential equation
I cannot instantly become zero!
Self-induction
like discharging a capacitor

20. Behavior of Inductors Increasing Current Decreasing 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.

21. The switch in this circuit is initially open for a
Physics :30 –Quiz 2
The switch in this circuit is initially open for a
long time, and then closed at t = 0. What is the
magnitude of the voltage across the inductor
just after the switch is closed?
zero V
R / L
V / R 2V

22. Physics :30 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?
zero V
R / L
V / R 2V

23. Physics 241 –Quiz C
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?
zero
V / L
R / L
V / R
2V / R

24. Warm up quizzes for Thursday Lecture
Which of the following statement is true? A. B. C. D.