1. General Physics (PHY 2140) Lecture 16 Electricity and Magnetism
Induced voltages and induction
Magnetic flux and induced emf
Faraday’s law
Chapter 20
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2. Lightning Review Last lecture: Magnetism Ampere’s law and applications
Induced voltages and induction
Magnetic flux
Review Problem: A sphere of radius R is placed near a long, straight wire that carries a steady current I. The magnetic field generated by the current is B. The total magnetic flux passing through the sphere is
1. moI.
2. moI /(4 pR2).
3. 4 pR2 moI
4. zero.
5. need more information
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3. Recall: right hand rule II
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4. 20.1 Induced EMF and magnetic flux
Faraday’s experiment
Two circuits are not connected: no current?
However, closing the switch we see that the compass’ needle moves and then goes back to its previous position
Nothing happens when the current in the primary coil is steady
But same thing happens when the switch is opened, except for the needle going in the opposite direction…
Picture © Molecular Expressions
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What is going on?

5. 20.2 Faraday’s law of induction
Induced current I N S v
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6. 20.2 Faraday’s law of inductionv B I N S I
A current is set up in the circuit as long as there is relative motion between the magnet and the loop.
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7. Does there have to be motion?
AC Delco - +
1 volt I I
(induced)
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8. Does there have to be motion?
AC Delco - +
1 volt
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9. Does there have to be motion?
AC Delco - +
1 volt I
(induced)
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10. Does there have to be motion?
NO!!
Does there have to be motion?
AC Delco - +
1 volt
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11. Maybe the B-field needs to change…..v B
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12. Maybe the B-field needs to change…..v B
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13. Maybe the B-field needs to change…..v B I
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14. Faraday’s law of magnetic induction
In all of those experiment induced EMF is caused by a change in the number of field lines through a loop. In other words,
The instantaneous EMF induced in a circuit equals the rate of change of magnetic flux through the circuit.
Lenz’s Law: The polarity of the induced emf is such that it produces a current whose magnetic field opposes the change in magnetic flux through the loop. That is, the induced current tends to maintain the original flux through the circuit.
Lenz’s law
The number of loops matters
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15. Applications: Ground fault interrupter Electric guitar SIDS monitor
Metal detector …
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16. Example 1: EMF in a loop
A wire loop of radius 0.30m lies so that an external magnetic field of strength +0.30T is perpendicular to the loop. The field changes to -0.20T in 1.5s. (The plus and minus signs here refer to opposite directions through the loop.) Find the magnitude of the average induced emf in the loop during this time.
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17. and after the field changes the flux is
A wire loop of radius 0.30m lies so that an external magnetic field of strength +0.30T is perpendicular to the loop. The field changes to -0.20T in 1.5s. (The plus and minus signs here refer to opposite directions through the loop.) Find the magnitude of the average induced emf in the loop during this time.
Given:
r = 0.30 m
Bi = 0.30 T
Bf = T
Dt = 1.5 s
Find:
EMF=?
The loop is always perpendicular to the field, so the normal to the loop is parallel to the field, so cosq = 1. The flux is then
Initially the flux is
and after the field changes the flux is
The magnitude of the average induced emf is:
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18. Example 2: EMF of a flexible loop
The flexible loop in figure below has a radius of 12cm and is in a magnetic field of strength 0.15T. The loop is grasped at points A and B and stretched until it closes. If it takes 0.20s to close the loop, find the magnitude of the average induced emf in it during this time. A
X X X X B
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19. 20.3 Motional EMF l v B F
Let's consider a conducting bar moving perpendicular to a uniform magnetic field with constant velocity v.
This force will act on free charges in the conductor. It will tend to move negative charge to one end, and leave the other end of the bar with a net positive charge.
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20. Motional EMF
The separated charges will create an electric field which will tend to pull the charges back together.
When equilibrium exists, the magnetic force, F=qvB, will balance the electric force, F=qE, such that a free charge in the bar will feel no net force.
Thus, at equilibrium, E = vB. The potential difference across the ends of the bar is given by DV=El or
A potential difference is maintained across the conductor as long as there is motion through the field. If the motion is reversed, the polarity of the potential difference is also reversed.
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21. Motional EMF – conducting railsv Dx B
We can apply Faraday's law to the complete loop. The change of flux through the loop is proportional to the change of area from the motion of the bar:
or (Faraday’s law)
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current
Motional EMF

22. Example: wire in the magnetic field
Over a region where the vertical component of the Earth's magnetic field is 40.0µT directed downward, a 5.00 m length of wire is held in an east-west direction and moved horizontally to the north with a speed of 10.0 m/s. Calculate the potential difference between the ends of the wire, and determine which end is positive.
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23. 20.4 Lenz’s law revisited
Application of Lenz's law will tell us the direction of induced currents, the direction of applied or produced forces, and the polarity of induced emf's.
Lenz's law says that the induced current will produce magnetic flux opposing this change. To oppose an increase into the page, it generates magnetic field which points out of the page, at least in the interior of the loop. Such a magnetic field is produced by a counterclockwise current (use the right hand rule to verify).
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24. Lenz’s law: energy conservation
We arrive at the same conclusion from energy conservation point of view
The preceding analysis found that the current is moving ccw. Suppose that this is not so.
If the current I is cw, the direction of the magnetic force, BlI, on the sliding bar would be right.
This would accelerate the bar to the right, increasing the area of the loop even more.
This would produce even greater force and so on.
In effect, this would generate energy out of nothing violating the law of conservation of energy.
Our original assertion that the current is cw is not right, so the current is ccw!
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25. S S S N S N N v v The induced flux seeks to counteract the change.
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26. Example: direction of the current
Find the direction of the current induced in the resistor at the instant the switch is closed.
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27. Applications of Magnetic Induction
Tape / Hard Drive / ZIP Readout
Tiny coil responds to change in flux as the magnetic domains (encoding 0’s or 1’s) go by.
Question: How can your VCR display an image while paused?
Credit Card Reader
Must swipe card
 generates changing flux
Faster swipe  bigger signal
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