Electromagnetic Induction

Magnetic Fields Can Move Charges A moving charge or a group of moving charges (a

current) produce a magnetic field—flowing current will deflect a magnet

Magnets can cause forces on moving charges—a magnetic field can deflect a current carrying wire

This force is always at right angles to the current and the magnetic field

Voltage in Wires Moving in Magnetic Fields   

Charges at ends of rodexert electrostatic forceon any charge q in rod.

V = vBL  

Magnetic Force on Induced Current 

Magnetic force to the left resists push to the right by the hand.

 F = IBL

A Current Generator 

The First Generator

Michael Faraday  (1791-1867)

Magnetic Flux

Φ = BA

Φ  = BA cos θ

Changing Flux

Wire is pulled to the right by an unseen force.              Induced emf = vBL

Changing Flux and Faraday's Law

Φ = BA                 (1)

∆Φ = ∆ (BA)            (2)       = BA               (3)       = B(L∆x)           (4) ∆Φ / ∆ t  = BL ∆ x / ∆ t      (5)             = BLv              (6)

Faraday's Law: The induced emf in a singlecoil of wire is                                      ∆Φ / ∆ t

If there is a stack of N loops of wire, then the induced emf is N times as great:

Induced emf  =  N/t

Faraday's Law Example

Induced emf =/t           = BA

This time, changes because the B-field changes.

= B)A                        ----------------------------------Example:  B0 = 0.04 T              

                  B  = 0.07 T              B  = 0.03 T                   A = 0.004 m2

                  t = 0.005 s                = (0.03)(0.004)                       = 1.2 x 10-3 T-m2

Induced emf = /t                     = 1.2 x 10-3 /0.005                     = 0.24 V

Faraday's Law Examples

Flux through coil changes because barmagnet is moved up and down. 

AC current in bottom coil causes changing B-field along iron core.

Flux Changing by Changing Areas

= BA                    (1) = B          (2)

Magnetic field doesn'tchange; area changes.

The more quickly theloop is stretched, the smaller will be t and the larger will be the transient emf

Induced emf = /t

Do Now (1/24/14):

1. What is Faraday’s Law?

2. A magnetic field increases by 2T over a time of 5 s. The magnetic field is enclosed by a circular loop of diameter 5 cm. What is the induced EMF in the wire?

Changing Magnetic Fields Cause Changing Flux

This is the field of the induced current.

changes in this casebecause the magnet isbrought closer to the loop; consequently, more B arrows penetrate the plane |of the loop.

Flux increases.

Induced emf = /t

Changing Magnetic Fields

This is the field of the induced current.

Magnet is removed from the loop; consequently, fewer B arrows penetrate the plane|of the loop.

Flux decreases. Induced emf = /t

Practice:

Work with your peers on the three AP problems. We will finish working on them on Monday.

Radio Antenna Uses Faraday's Law

Radio waves are electromagnetic.  The oscillating B-field of the EM waves induce an emf in the coil.

The Induction Stove

• A changing flux through the bottom of the metal pot generates an emf which causes current to circulate around the bottom of the pot.

• I2R heat is dissipated in metal pot, but not in the glass pot or the stove top because they're insulators.

Ground Faults Current takes shorter path to

ground by going through hand, arm and legs of the person.

A properly grounded wire will prevent this. Faulty grounding can be overcome by a "ground-fault circuit interrupter" (GFCI or GFI)

Ground Fault Circuit Interrupters Explained

Net current through iron ring is zero unless there'sa short in the circuit.

If the return current is lessthan the entering current,a magnetic field will besuddenly be created in the iron ring, and thischanging field will inducean emf in the sensing coil..

Electric Guitar's Pick-Up Coil

Vibrating string changes flux through coil, inducing an emf which oscillates in rhythm with the guitar string

Playback Read Head in a Tape Player -- Moving Coil Microphone

Iron core becomes magnetized, causing the flux through the coil to change

Fluctuating air pressure moves diaphragm with coil attached alternately toward and away from magnet

Writing Data on Magnetic Disk

Lenz's Law

Magnet is brought closer, increasing the number of B-field penetrations of the plane of the loop.

Cause:  Magnet moving to the right

Effect:  Coil becomes an electromagnet             to oppose movement of bar.

Rule:  "see counterclockwise, see north"

Another way to look at it:

Cause:  More B-arrows puncture plane

Effect:  Induced electromagnet creates             its own B-field arrows pointing             in the opposite direction, partially             canceling the increase. 

An induced emf always gives rise to a current whose magnetic field opposes the original change in flux

Practice:

Work with your peers on the three AP problems. We will finish working on them on Monday.

Do Now (1/27/14):

Use last week’s Do Now sheet, please!!! In your own words, describe Lenz’s Law

DO NOT TOUCH MATERIALS UNTIL INSTRUCTED TO DO SO!!!

Copper Tube Demo

1. Theoretically, if you drop the pencil and the magnet at the same time, which will hit the ground first and why?

2. Predict what will happen if you drop your pencil inside the tube.

3. Predict what will happen if you drop the magnet inside the tube.

Copper Tube Demo

Please DO NOT drop the magnets!!!

1. Is the magnet attracted to the copper tube? Why or why not?

2. Drop your pencil inside of the copper tube. Is this faster or slower than you would expect from normal free fall? Why?

3. Describe what happens as the magnet falls through the copper tube. Make a guess as to why this occurs.

Review: Lenz’s Law

When an emf is generated by a change in magnetic flux according to Faraday's Law, the polarity of the induced emf is such that it produces a current whose magnetic field opposes the change which produces it. The induced magnetic field inside any loop of wire always acts to keep the magnetic flux in the loop constant.

Review: Lenz’s LawLenz’s Law:  In the examples below, if the B field is increasing,

the induced field acts in opposition to it. If it is decreasing, the induced field acts in the direction of the applied field to try to keep it constant..

Lenz's Law

Magnet is taken away from the loop, decreasing the number of B-field penetrations of the plane of the loop.

Cause:  Magnet moving  away, to the left

Effect:  Coil becomes an electromagnet to attract back the bar magnet.

Rule:  "see clockwise, see south"

Another way to look at it:

Cause:  Fewer B-arrows puncture plane

Effect:  Induced electromagnet creates its own B-field arrows pointing in the  same direction as the bar magnet's field,  partially canceling the loss of B arrows.

Lenz's Law

Cause:  Increase in flux Effect:   Induced current in loop creates a magnetic             field (not shown) which partially cancels flux

A second way to look at it:

The induced current as viewed from the left is clockwise, making the left face of loop the south pole, which is repelled by the south pole of the electromagnet.

(Effect opposes cause.)

A third way:

Growth of counter-clockwise current is opposed by growth of clockwise current.

Lenz's Law Cause:  Decrease in flux

Effect:   Induced current in loop              creates a magnetic field              (not shown) which               partially restores flux

Lenz's Law

Ring on left acts like a magnet with a north face on top to repel the falling magnet (effect opposing cause)

As viewed from above is current in ring clockwise, or counter-clockwise?

“See counterclockwise, see north"

What happens in the split ring?

Lenz's Law

Cause:  bar magnet movingaway.

Effect:  induced electromagnet's polarity will be such that it will try to attract the magnet back.

What will be the polarity, north, or south, of the left face of theinduced electromagnet?

Lenz's Law

Current is suddenly established in wire at bottom.  What isthe direction--clockwise, or counterclockwise--in the loop?

Lenz's Law

What will be the direction of the current in the resistor when the switch is closed?  Hint:  what will be the polarity of the right face of the first magnet?

Faraday's and Lenz's Laws 

An emf is generated onlyif the flux is changing.

Note that current is zero while the loop is completely inside themagnetic field.

Practice:

Continue working with your peers on the AP practice problems. We will discuss them and grade them as a class.

Do Now (1/28/14):Consider a flat square coil with N = 5 loops. The

coil is 20 cm on each side, and has a magnetic field of 0.3 T passing through it. The plane of the coil is perpendicular to the magnetic field: the field points out of the page.

(a) If nothing is changed, what is the induced emf?

(b) The magnetic field is increased uniformly from 0.3 T to 0.8 T in 1.0 seconds. While the change is taking place, what is the induced emf in the coil?

Do Now (solutions)

A.

Do Now (solutions) B. Probably the most straight-forward way

to approach this is to calculate the initial and final magnetic flux through the coil.

The induced emf is then:

Taking it Further:

(c) While the magnetic field is changing, the emf induced in the coil causes a current to flow. Does the current flow clockwise or counter-clockwise around the coil?

Taking it Further: Apply Lenz's law, as well as the right-hand rule. While the magnetic field is being changed, the

magnetic flux is being increased out of the page. According to Lenz's law, the emf induced in the loop by this changing flux produces a current that sets up a field opposing the change.

The field set up by the current in the coil, then, points into the page, opposite to the direction of the increase in flux.

To produce a field into the page, the current must flow clockwise around the loop. This can be found from the right hand rule.

Lenz’s Law:

Taking it Further:

One way to apply the rule is this: Point the thumb on your right hand in the direction of the required field, into the page in this case. If you curl your fingers, they curl in the direction the current flows around the loop - clockwise.

AC Generator Explained

Electrons in opposite sides of loop are moving  in opposite directions, so theforces on them are oppositely directed.

A half-cycle later, those electrons aremoving in the opposite direction.

Electric Generator 

Counter Torque    

Principles of Transformer Action 

Iron Core Transformer 

This is a "step-up" transformer because the voltage is increased

Power Transmission and Transformers

Output power = IV--------------------

Why is output at low current and high voltage, and not high current andlow voltage?--------------------

Answer:  I2R losses

 Automobile Ignition System

Spark plug gap is about 1/50 inch (0.020 in), or about 1/20 cm.

Breakdown strength of air is30,000 V/cm, so 1500 V is required across the 1/20 cmspark plug gap.

If there are 1000 turns on the primary, how many turns mustthe secondary have?

Transformer Station and Telephone Pole Transformer 

Steps down from 240,000 V to 8000 V

Steps down from 8000 V to 240 V