1. Conclusion – Chapter 20 & Chapter 21 – Electromagnetic induction
Presentation slide for courses, classes, lectures et al.
Chapter 21

2. Quick Review IB r
Magnetism

3. Force Between Two Current Carrying Conductors
First wire produces a magnetic field at the second wire position.
The second wire therefore feels a force = Bil
Magnetism

4. Solenoid
B=~0 outside
Magnetism

5. The Toroid–
B=0 outside
Magnetism

6. A rectangular loop has sides of length 0. 06 m and 0. 08 m
A rectangular loop has sides of length 0.06 m and 0.08 m. The wire carries a current of 10 A in the direction shown. The loop is in a uniform magnetic field of magnitude 0.2 T and directed in the positive x direction. What is the magnitude of the torque on the loop?
8 × 10–3 N × m
Magnetism

7. A solenoid of length 0. 250 m and radius 0
A solenoid of length m and radius m is comprised of 440 turns of wire. Determine the magnitude of the magnetic field at the center of the solenoid when it carries a current of 12.0 A.
2.21 × 10–3 T
Magnetism

8. The drawing shows two long, thin wires that carry currents in the positive z direction. Both wires are parallel to the z axis. The 50-A wire is in the x-z plane and is 5 m from the z axis. The 40-A wire is in the y-z plane and is 4 m from the z axis. What is the magnitude of the magnetic field at the origin?
3 × 10–6 T
Magnetism

9. Moving On to the next chapter……………….
Magnetism

10. INTRODUCTION TO INDUCTION
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11. Important Definition – Magnetic Flux
Magnetic Field
AREA
Induction
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12. Induction
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13. The Essence of this Topic
Consider a conductor that is shaped in a loop but is continuous.
The conductor has a magnetic field through the loop that is not necessarily uniform.
There is a MAGNETIC FLUX through this loop.
If the FLUX CHANGES, an “emf” will be induced around the loop.
This emf can cause a current to flow around the loop.
Induction
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14. How Can You Change the Magnetic Flux Going Through The Loop? Huh?
Divide the area of the loop into a very large number of small areas DA.
Find the Magnetic Field through each area as well as the angle that it makes with the normal to the area.
Compute the total flux through the loop.
Induction
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15. The Magnetic Flux Going Through The Loop:
Add up all of these pieces
that are INSIDE the loop.
Induction
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16. Changing F Change any or all of the And the Flux will change! Bi DAifi
Change the SHAPE of the loop
Change the ANGLE that the loop makes with the magnetic field (subset of above)
And the Flux will change!
Induction
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17. WAIT A SECOND ……. You said that there is a conducting loop.
You said that there is therefore a VOLTAGE or emf around the loop if the flux through the loop changes.
But the beginning and end point of the loop are the same so how can there be a voltage difference around the loop?
‘tis a puzzlement!
Induction
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18. Induction
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19. REMEMBER when I said E Fields start and end on CHARGES???
DID I LIE??
Induction
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20. BUT WAIT, YOU STILL LIE! The truth
Electric fields that are created by static charges must start on a (+) charge and end on a (–) charge as I said previously.
Electric Fields created by changing magnetic fields can actually be shaped in loops.
BUT WAIT, YOU STILL LIE!
Induction
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21. Why do you STILL think I am a liar?
Because you said that an emf is a voltage so if I put a voltmeter from one point on the loop around to the same point, I will get ZERO volts, won’t I
Induction
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22. Yes … but this doesn’t make me a liar! Let Me Explain.
Induction
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23. The POTENTIAL between two points
Is the WORK that an external agent has to do to move a unit charge from one point to another.
But we also have (neglecting the sign): Ds
Induction
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24. So, consider the following:
x x x x x x x E
Conductor
Induction
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25. THEREFORE WHAT WILL A VOLTMETER READ FROM A to A?
x x x x x x x
A The emf
B Zero
C Can’t tell E  A
Conductor
Induction
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26. How Big is the emf? Faraday’s Law
Michael Faraday ( )
MINUS????
Induction
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27. Q: Which way does E point?
A: The way that you don’t want it to point! (Lenz’s Law).
Lenz’s Law Explains the (-) sign!
Induction
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28. OK. LET’S DO THE PHYSICS NOW
Induction
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29. DEMOs
Induction
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30. Is there an induced current???
Induction
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31. A changing magnetic field INDUCES a current in a circuit loop.
Induction Effects
A changing magnetic field INDUCES
a current in a circuit loop.

32. Faraday’s Experiments?

33. Insert Magnet into Coil

34. Remove Coil from Field Region

35. Summary

36. Does the Flux Change?
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37. In the Previous Example, if there are N coils rather than a single coil,
A The current is increased by a factor of N
B The current is decreased by a factor of N
C The current stays the same.
Induction
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38. Push a magnet into a coil of two wires and a current is produced via an emf.
In this case, 2 coils, each has the SAME emf.
Ohm’s Law still works, so
Induction
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39. If we go from 2 to 4 coils, the current
A Stays the same
B Doubles
C Is halved
D Is four times larger
Induction
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40. A rectangular circuit containing a resistor is perpendicular to a uniform magnetic field that starts out at 2.65 T and steadily decreases at 0.25 T/s. While this field is changing, what does the ammeter read?
Induction
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41. ••The conducting rod ab shown makes frictionless contact with metal rails ca and db. The apparatus is in a uniform magnetic field of T, perpendicular to the plane of the figure. (a) Find the magnitude of the emf induced in the rod when it is moving toward the right with a speed 7.50 m/s.
Induction
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42. Application: AC Voltage Generator
Induction
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43. Almost DC
Induction
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44. The Strange World of Dr. Lentz

45. Lenz’s Law
Induced Magnetic Fields always FIGHT to stop what you are trying to do!
i.e... Murphy’s Law for Magnets

46. Example of Nasty Lenz The induced magnetic field opposes the
field that does the inducing!

48. Don’t Hurt Yourself!
The current i induced in the loop has the direction
such that the current’s magnetic field Bi opposes the
change in the magnetic field B inducing the current.

49. Let’s do the
Lentz Warp
again !

50. Again: Lenz’s Law An induced current has a direction
such that the magnetic field due to
the current opposes the change in
the magnetic flux that induces the
current. (The result of the negative sign that we always leave out!) … OR
The toast will always fall buttered side down!

51. What Happens Here?
Begin to move handle as shown. Assume a resistance R in the loop.
Flux through the loop decreases.
Current is induced which opposed this decrease – current tries to re- establish the B field.

52. What about a SOLID loop?? Eddy Currents Energy is LOST BRAKING SYSTEM
METAL
Pull
Eddy Currents

53. The current in winding A is directed
A cardboard tube is wrapped with two windings of insulated wire, as shown. Is the induced current in the resistor R directed from left to right or from right to left in the following circumstances?
The current in winding A is directed
(a) from a to b and is increasing,
(b) from b to a and is decreasing,
(c) from b to a and is increasing, and
(d) from b to a and is constant.
left right
Induction
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54. Mutual inductance – Suppose i1 CHANGES
Flux Changes
Circulation of currents in one coil can generate a field in the coil that will extend to a second, close by device.
Suppose i1 CHANGES
Current (emf) is
induced in 2nd
coil.

55. The two coils Remember – the magnetic field outside of the solenoid
is pretty much zero.
Two fluxes (fluxi?) are the same!
Induction
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56. Self-inductance –
Any circuit which carries a varying current self-induced from it’s own magnetic field is said to have INDUCTANCE (L).

57. An inductor resists CHANGES in the current going through it.
Induction
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58. An inductor resists CHANGES in the current going through it.
Induction
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59. An inductor resists CHANGES in the current going through it.
Induction
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60. Faraday says this is the emf!
Inductance Defined
If the FLUX changes a but during a short time Dt, then the current will change by a small amount Di.
Faraday says this is the emf!
This is actually a
calculus equation
Induction
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61. So … E= The UNIT of “Inductance – L” of a coil is the henry. SYMBOL:
There should be
a (-) sign but we
use Lenz’s Law
instead!
The UNIT of “Inductance – L” of a coil is the henry.
SYMBOL:
Induction
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62. Induction
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63. Consider “AC” voltage Minimum Change/Dt V1 Maximum Change/Dt Induction
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64. FLUX is the same through
The transformer
FLUX is the same through
both coils (windings).
Induction
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65. Induction
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66. Induction
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67. Input/Output Impedance (Resistance)
Induction
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68. Read in the textbook section 21.10:
Induction
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69. Energy associated with an induced current.
As energy is introduced at induces a field, energy is stored in an electronic device.
Refer to worked example in your text.

70. The R-L circuit – Figure 21.29
When an inductor is part of a wired circuit, - voltages, currents and capacitor charges are a function of time, not constants.
Refer to worked example in your text.

71. The L-C circuit – Figure 21.34
When an inductor is part of a wired circuit with a capacitor, the capacitor charges over time.
Commonly used in radio as a tuner for the induced current from an antenna.