Electromagnetic Inductionand Electromagetism

Chapter 25 and 26

Nt

E

• Electric currents produce magnetic fields (Oersted’s experiments)• “While performing his electric demonstration, Oersted noted to

his surprise that every time the electric current was switched on, the compass needle moved. He kept quiet and finished the demonstrations, but in the months that followed worked hard trying to make sense out of the new phenomenon.”

• Is the opposite true: can magnetic fields create electric currents?

Faraday’s experiments• Faraday discover the answer…..• On August 29, 1831, Faraday

wound a thick iron ring on one side with insulated wire that was connected to a battery. He then wound the opposite side with wire connected to a galvanometer.

• He closed the primary circuit and, to his delight and satisfaction, saw the galvanometer needle jump.

• When he opened the circuit, however, he was astonished to see the galvanometer jump in the opposite direction.

• In the fall of 1831 Faraday attempted to determine just how an induced current was produced.

Faraday’s experimentsFaraday is thought of as one of the greatest experimentalist of all time. He developed many important devices including the Faraday cage, the first dc generator and the first ac generator

Induced current• When a magnet approaches a coil of wire, the magnetic field becomes

stronger, and it is this changing field that produces the current.• The current in the coil is called induced current because it is brought

about by a changing magnetic field.

NSvI

Induced EMF

NSI

v

v

B

B

I

I

• Since a source of emf is always need to produce a current, the coil itself behaves as if it were a source of emf. This emf is known as an induced emf.

A current is set up in the circuit as long as there is relative motion between the magnet and the loop.

Back to Faraday’s two coils of wire

AC Delco- +

1 volt

I

If you have a current flowing through one coil and no current in a second coil which is not touching the first, then………

AC Delco- +

1 volt

I(induced)

Back to Faraday’s two coils of wire

open the the switch (stop the current in the first), an induced current is brought about in the second coil. The coils do not need to touch or move relative to each other.

A current will also be induced (in the other direction) when the switch is closed again.

• In Faraday’s experiment, the current (moving charge) produces a magnetic field.

• When the current is turned off, the magnetic field changes and a current is induced in the other coil.

• The changing magnetic field brings about an induced current.• In the experiment shown below, again the changing magnetic

field brings about an induced current and induced emf.

Back to Faraday’s two coils of wire

• As the hand pushes the conducting rod, in a constant magnetic field, an induced current causes the light bulb to come on.

• In this case, the magnetic field is not changing, but there is still an induced current. Why?

Bv

I

I

Motional EMF

Motional EMF

Bv

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.

sinF qvB

l

F

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.

• So, at equilibrium, E = vB. The potential difference across the ends of the bar is given by V=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.

V El Blv

Motional EMF and forces

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

 If the rod moves at a constant speed, F = IBL, equals the magnetic force and the force on the hand, where I is the current, B is the magnetic field and L is the length of the conducting rod. (This force is the force on a current carrying wire in a magnetic field discussed in the magnetic fields power point presentation.)

L

Faraday’s Law• Faraday was able to explain

all three experiments with his law.

• Faraday’s Law: The instantaneous EMF induced in a circuit equals the rate of change of magnetic flux through the circuit.

Nt

E

= BA

cosThe number of loops matters

E

Magnetic flux• Place a loop in the B-field. The

flux, , is defined as the product of the field magnitude by the area crossed by the field lines.

• Units: T·m2 or Webers (Wb)• The value of magnetic flux is

proportional to the total number of magnetic field lines passing through the loop.

• Faraday said the induced emf depends on the rate of change of the flux, so a change in B or Area or a change in both can cause a flux change.

cosB A BA

B is the component of B perpendicular to the loop, is the angle between B and the normal to the loop and A is the area of the loop.

Faraday’s Law - ExampleThis 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 - Example

Induced emf = /t     (Omitting negative sign)

= BA                     = B          

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.

BlvI

R R E

Motional EMF-Faraday’s Law

Bv

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:

BA Bl x xBl Blv

t t

Eor (Faraday’s law)

current Motional EMF

x

R

EE

Lenz’s Law• Lenz’s Law allows for the determination of the

direction of the induced current, clockwise or counter clockwise

• 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.

Nt

E

Lenz’s law

Lenz’s Law - examples

• 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. In diagram A, to oppose an increase into the page, a magnetic field which points out of the page is generated, 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).

(A) (B)

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!

Lenz’s Law – more examplesCause:  More B-arrows puncture plane

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

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

Generators• A generator is a

device that that converts mechanical energy into electrical energy

• A coil is rotated in a magnetic field, as a result the coil has an alternating emf induced in it.

The First Generator

Simple Generator

Simple A.C. Generator• Consider a coil of wire rotating in a uniform magnetic field, B, as shown in

diagram A below.• When the coil is in the position shown in diagram A, side 2 is moving down

and side 1 is moving up and end q will (at that instant) be the positive terminal of the generator.

• When the coil has rotated through half a turn, end p will be the positive terminal.

• Therefore, a coil of wire rotating in a magnetic field has an alternating emf induced in it.

• To connect the coil to a light bulb (or any other component) brushes made of carbon make contact with slip rings made of brass, as shown in diagram B.

(A)

(B)

Generators

• In a hydroelectric plant the coil in the generator is turned by the waterfall.

• As the coil turns the induced emf changes as shown in the graph above.

Graph of induced emf against time

AC• AC stands for alternating current. Alternating Current (AC)

flows one way, then the other way, continually reversing direction.

• An AC voltage is continually changing between positive (+) and negative (-).

• Electric generators used in power plants produce AC current,• so AC current is the type of current that is in your home.

DC• DC stands for direct current. Direct Current (DC)

always flows in the same direction, but it may increase and decrease.

• A DC voltage is always positive (or always negative), but it may increase and decrease

• Cells, batteries and regulated power supplies provide steady DC which is ideal for electronic circuits

Transformer• A transformer is an

electrical device used to convert AC power at a certain voltage level to AC power at a different voltage, but at the same frequency. There are two kinds of transformers: step down and step up. Step up transformers increase the voltage where step down transformers decrease the voltage.

The First Generator

Step-up and Step-down Transformers

• Step-up example (pictured above): A picture tube in a TV needs about 15000 V to accelerate the electron beam that is needed for the picture, and a step-up transformer is used to obtain this high voltage from the 120 V wall socket.

• Step-down example: Only 3 – 9 V are needed to energize batteries. A step-down transformer is used to reduce the 120 ac voltage from the wall to a much smaller value.

• A transformer consists of a primary coil and a secondary coil both wound on an iron core.

• The changing magnetic flux produced by the current in the primary coil induces an emf in the secondary coil.

Electromagnetic Waves

• Faraday’s law states: An electric field is created in any region of space in which a magnetic field is changing with time. The magnitude of the induced electric field is proportional to the rate at which the magnetic field changes. The direction of the induced electric field is at right angles to the changing magnetic field.

• James Clerk Maxwell states: A magnetic field is created in any region of space in which an electric field is changing with time. The magnitude of the magnetic field is proportional to the rate at which the magnetic field changes. The direction of the induced magnetic field is at right angles to the changing electric field.

• The vibrating electric and magnetic fields in the diagram above regenerate each other to make up an electromagnetic wave (light), which emanates from a vibrating charge.

James Clerk Maxwell's Equations• James Clerk Maxwell.James

Clerk Maxwell is considered one of the most important physicists of the 19th century and of all time.

• His best-known discoveries concern the relationship between electricity and magnetism and are summarized in what has become known as Maxwell’s Equations, which have become a major underpinning of modern physics.

Maxwell’s four equations by themselves, define the entire field of electricity and magnetism

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

• If charges oscillate back and forth in the wire, you get a changing electric fields.

• If charges oscillate back and forth, you get changing magnetic fields too.

• If the fields are perpendicular, you have electromagnetic radiation.

Electromagnetic Waves: Radio waves

E

+++

+

Electromagnetic Waves: X-rays• X-ray production occurs whenever electrons of high energy strike a heavy metal

target, like tungsten or copper. When electrons hit this material, some of the electrons will approach the nucleus of the metal atoms where they are deflected because of their opposite charges (electrons are negative and the nucleus is positive, so the electrons are attracted to the nucleus). This deflection causes the energy of the electron to decrease, and this decrease in energy then results in forming an x ray.

Sources

• http://sol.sci.uop.edu/~jfalward/electromagneticinduction/electromagneticinduction

• http://www.physics.wayne.edu/~apetrov/PHY2140/#lectures

• Physics by Zitzewitz