Electromagnetic Induction

Ch. 29

Observations made during various induction experiments (first performed by Michael Faraday in the 1830’s:When there is no current in the

electromagnet, so that B = 0, the galvanometer shows no current.

When the electromagnet is initially turned on, there is a momentary current through the meter as B increases.

When B levels off at a steady value, the current drops to zero, no matter how large B is.

Further observations:With the coil in a horizontal plane, we squeeze

it so as to decrease the cross-sectional area of the coil. The meter detects current only during the deformation, not before or after. When we increase the area to return the coil to its original shape, there is current in the opposite direction, but only while the area of the coil is changing.

If we rotate the coil a few degrees about a horizontal axis, the meter detects current during its rotation, in the same direction as when we decreased the area. When we rotate the coil back, there is a current in the opposite direction during this rotation.

Even more observations: If we jerk the coil out of the magnetic field,

there is a current during the motion, in the same direction as when we decreased the area.

If we decrease the number of turns in the coil by unwinding one or more turns, there is a current during the unwinding, in the same direction as when we decreased the area. If we wind more turns onto the coil, there is a current in the opposite direction during the winding.

When the magnet is turned off, there is a momentary current in the direction opposite to the current when it was turned on.

And even more observations:The faster we carry out any of these

changes, the greater the current.If all these experiments are repeated with a

coil that has the same shape but different material and different resistance, the current in each case is inversely proportional to the total circuit resistance. This shows that the induced emfs that are causing the current do not depend on the material of the coil but only on its shape and the magnetic field.

Young and Freeman, pg. 1107

In conclusion,

In reviewing these statements, what is the common concept that exists??

Faraday's Magnetic Field Induction ExperimentWhen Michael Faraday made his

discovery of electromagnetic induction in 1831, he hypothesized that a changing magnetic field is necessary to induce a current in a nearby circuit. To test his hypothesis he made a coil by wrapping a paper cylinder with wire. He connected the coil to a galvanometer, and then moved a magnet back and forth inside the cylinder.

http://micro.magnet.fsu.edu/electromag/java/faraday2/

DefinitionElectromagnetic induction:

◦A changing magnetic flux through a circuit induces an emf and current in the circuit.

Faraday’s LawThe induced emf in a circuit is

proportional to the time rate of the change of magnetic flux through the circuit.

Recall:

http://phet.colorado.edu/simulations/sims.php?sim=Faradays_Electromagnetic_Lab

cos

B

B

d

dt

NBA

Examples of Faraday’s LawA bar magnet is

moved through a loop of wire that has a cross-sectional area of 0.004 sq. m. The magnetic field changes from 0.04 T to 0.07 T in 0.005 s. Calculate the magnitude of the induced emf.

More Faraday’s Law Examples

Flux through coil changes because bar magnet is moved up and down.

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

Flux Changing by Changing AreasMagnetic field doesn’t change;

area changes. The more quickly the loop is stretched, the larger the induced emf.

Changing Magnetic Fields Cause Changing FluxAs the magnet approaches the

loop, the more B-field lines penetrate the loop causing the flux to increase.

In the opposite directionAs the magnet is moved away

from the loop, the number of B-field lines decrease and the flux decreases.

Lenz’s LawStates that the polarity of the

induced emf is such that it tends to produce a current that creates a magnetic flux to oppose the change in magnetic flux through the area enclosed by the current loop, or in other words, the direction of any magnetic induction effect is such as to oppose the cause producing it.

Lenz’s LawAs the magnet is brought closer, increasing the number of field line penetrating 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 cancelling the increase.           

Lenz’s 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 cancelling 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 "See counterclockwise,

see north"---------------------------------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?---------------------------------What happens in the split ring?

Lenz’s LawCause:  bar magnet moving away. 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 the induced electromagnet?

Lenz’s LawCurrent is suddenly established

in wire at bottom.  What is the direction--clockwise, or counter clockwise--in the loop?

Lenz’s LawWhat 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 & Lenz’s LawsAn emf is generated only if the

flux is changing. Note that current is zero while the loop is completely inside the magnetic field. Why?

Motional emf

Charges at ends of rod exert electrostatic force on any charge q in rod.

At equilibrium,  Fe = Fm            qE = Fm              qE = qvB              E = vB              

Recall, E =  ΔV /Δs        

ΔV= E Δs                = vBL             (induced emf)

ΔV = vBL  

Magnetic force on induced currentMagnetic force to the left resists push to the right by the hand.

Induced emf and Electric Fields

We have seen that a changing magnetic flux induces an emf and a current in a conducting loop. Therefore, we must conclude that an electric field is created in the conductor as a result of the changing magnetic flux.

The induced electric field is non-conservative and time varying.

Induced E-Field created by increasing B-FieldThe E-Field lines

form a vortex or "eddy".

An induced emf exists in a circular pattern.

To move the charges once around, the work done is

(2 )q qE r

Induced E-Fields

From Faraday’s law,

(2 )q qE r

2

2

1 1 ( )

2 2

2

B

Er

d d B rE

r dt r dt

r dBE

dt

Induced E-FieldsThe negative sign indicates that

the induced electric field opposes the change in the magnetic field.

In general form, Faraday’s law of induction,

BdE dl

dt

Induced E-FieldsIt is important to recognize that

the induced electric field is a non-conservative, time-varying field that is generated by a changing magnetic flux.

Motors & Generators

Motors Generators

Convert electrical energy into mechanical energy

As the coils turn in the magnetic field, an induced emf is created that produces an induced current in the reverse direction.

This is known as the ‘generator effect.’

Convert mechanical energy into electrical energy

Once there is a current in the loop, there exists a torque that acts on the loop in the opposite direction of the motion

This is known as the ‘motor effect.’

Maxwell’s EquationsFour equations, formulated by

James Clerk Maxwell, that together form a complete description of the production and interrelation of electric and magnetic fields. The statements of these four equations are (1) electric field diverges from electric charge, (2) there are no isolated magnetic poles, (3) electric fields are produced by changing magnetic fields, and (4) circulating magnetic fields are produced by changing electric fields and by electric currents. Maxwell based his description of electromagnetic fields on these four statements.

Maxwell’s EquationsGauss’s Law

Gauss’s Law forMagnetism

Faraday’s Law

Ampere’s Law

0

enclosed

o

B

o enclosed

qE dA

B dA

dE dl

dt

B dl I