Magnetism• Magnetic Poles: A magnet is a material that

creates a magnetic field. All magnets have two ends, a north and south pole.

• Magnetic fields cause certain types of material to become “magnetically polarized”

• A magnetically polarized material is a material where the “domains” inside have a magnetic “dipole moment,” that is held rigidly in place. Groups of molecules inside the substance are like little magnets, each with a north and south pole. and when the material becomes polarized, these line up together, producing a larger, stronger magnet.

Magnetic Materials• Ferromagnetic materials have a large and

positive susceptibility to an external magnetic field. They exhibit a strong attraction to magnetic fields and are able to retain their magnetic properties after the external field has been removed. Ferromagnetic materials have some unpaired electrons so their atoms have a net magnetic moment. They get their strong magnetic properties due to the presence of magnetic domains.

• Permanent magnets are all ferromagnetic materials

Paramagnetic Materials• Paramagnetic metals have a small and

positive susceptibility to magnetic fields. These materials are slightly attracted by a magnetic field and the material does not retain the magnetic properties when the external field is removed. Paramagnetic properties are due to the presence of some unpaired electrons and from the realignment of the electron orbits caused by the external magnetic field. Paramagnetic materials include magnesium, molybdenum, lithium, and tantalum.

Diamagnetic Materials• Diamagnetic metals have a very weak and

negative susceptibility to magnetic fields. Diamagnetic materials are slightly repelled by a magnetic field and the material does not retain the magnetic properties when the external field is removed. Diamagnetic materials are solids with all paired electron and, therefore, no permanent net magnetic moment per atom. Diamagnetic properties arise from the realignment of the electron orbits under the influence of an external magnetic field. Most elements in the periodic table, including copper, silver, and gold, are diamagnetic.

Magnetic Fields of Magnets• Like electric fields, magnetic fields are

indicative of lines of force. If you were to sprinkle iron filing around a magnet, the shape the filings would fall into naturally show the lines of the magnetic field.

• Also like electric field, magnetic field lines outside the magnet always have a defined direction: from the north pole of the magnet to the south pole.

• Inside the magnet the field lines run from the South pole to the North Pole.

Electromagnetism• Currents produce magnetic fields.• A current carrying wire produces a

magnetic field around the entire length of the wire. You can observe this phenomena with a compass.

• Compasses employ a strip of ferromagnetic material that aligns itself with the magnetic field of the planet. If a compass is placed near a wire carrying a current, the compass needle will deflect and align with the magnetic field.

Magnetic Dipoles• All magnetic sources act as a dipole, that is a

North and South pole. The simple reason for this is that B-field lines are continuous inside and outside any magnetic structure.– NS outside, SN inside

• There is no such thing as a magnetic monopole. When a bar magnet is split in two, the result is two smaller bar magnets.

• Even when magnetic materials are separated at the microscopic level, a dipole is formed. It is impossible to create a magnetic monopole.

B-Fields

• Magnetic Field: A force field created by the presence of a magnetic material or any moving charge such as a current. Magnetic fields create forces on charged particles and objects and induce currents in conductive materials.

• Symbol: B The magnetic field is a vector. It always has a direction.

• Unit: Tesla (T)

Current Carrying Wiresand the Right Hand Rule (RHR)

Magnetic Field of Coil(Solenoid)

What is the direction of current in this solenoid?

REMEMBER: The B-Field inside the magnet flows from the South Pole to the North Pole.

Electromagnets

• An electromagnet is a solenoid wrapped around a ferromagnetic (usually iron) core. The core has the effect of amplifying the B-field of the solenoid further, producing a stronger magnet with same current.

Why does this “amplifying effect” occur?

The intensity of a B-Field due to currents

• Geometry and matter can both affect the strength of a B-field, but in general:

• For a very long, straight wire:

r

iB

r

iB o

2

Magnetic ForcesForce on a single charge

• The force on a positively charged particle (test charge) in a magnetic field (B) is given by the equation:

Where q is the quantity of charge, v is the velocity of the charge and B is the magnitude of the magnetic field. The x is the operation “cross product,” basically a multiplication operation for vectors where direction is taken into account.

For circumstances where the B-Field is at a right angle to the moving charge (current) this equation can be re-written as:

F qv B

F qvB

Force on a current carrying wire• In the case of a wire carrying a current, the

force on the wire by an external magnetic field is given by the equation

Where i is the current in the wire, L is the length of the wire and B is the magnetic field. As with the prior example, when the length of wire in question is perpendicular to the magnetic field. The equation becomes:

F iL B

F iLB

Why do we care?• Electric motors work as a result of this

principle.• Electric generators employ the reverse of

this principle (electromagnetic induction), which we will study later.

• The use of electric current to produce a force and the reverse principle, the use of a mechanical force to produce an electric current, are foundational to modern technology.– Examples?

Representing a B-field

• Since current carrying wires create a magnetic field that wraps around the wire, perpendicular to every point on the surface, we need a way to draw B-fields near wires since we are restricted to a 2-D page.

Questions• 1)   A wire carries a current of 4.0 amps. The wire

is at right angles to a uniform magnetic field and 0.50 meters of the wire is in the field. The force on the wire is 0.62 Newtons. What is the strength of the magnetic field?

• 2) A high-speed electron travels at right angles to a magnetic field that has an induction of 0.620 Tesla. The electron is traveling at 3.46 x 107 m/s. What is the force acting on the electron?

Faraday’s Discovery• We have worked with the idea that currents

always produce magnetic fields.

• Now, we have already used this principle in our discussion of inductors, but we will expand now upon the reverse of the above principle.

• Faraday discovered that magnetic fields create induced currents.

In a nutshell:

When a conductor is either moved through a B-field, or a conductor is already inside a B-field when that field begins changing, there is an induced electric field inside the conductor that produces a current. This current will produce a magnetic field to offset the change in the external field.

Electromagnetic induction

• Connect a wire to both terminals of an ammeter. Now take a horseshoe magnet (or two opposite facing bar magnets) and move a wire vertically in between the poles. The needle in the ammeter will jump when the wire enters the strong B-field.

• As we discussed earlier, there will also be a resulting force on the wire.

Direction of current• Use the right hand rule to determine the

direction of the induced current in the wire.– Put your fingers in the direction of the B-field

and your thumb in the direction of the motion of the wire.

– The direction of your palm (imagine an arrow straight out, perpendicular from the palm of your hand) gives the direction of the force on the wire from the B-field.

– Recall that F=iLB, current in the wire is in the same direction as the force.

Electromotive force• When you pass a wire of velocity v through a

magnetic field, the B-field produces a current in the wire. But we know that in order for current to flow we must have a potential difference or voltage between the ends of the wire. The B-field actually creates this voltage.

• In the case where a current is induced in a wire by a B-field, the voltage create is referred to as an electromotive force.

• You might recall that we referred to a voltage source in a circuit as providing the “push” that causes electrons to flow in the wires. The two terms, voltage and Emf, are synonymous.

• EMF = BLv– B is the magnitude of the magnetic field, L is

the length of the wire in the field and v is the velocity of the wire as it passes through the field.

– The above equation is only true when the wire moves through the field perpendicular to the field. If it moves through at an angle, on the component of the wires velocity perpendicular to the field is involved in generating the EMF.

Faraday/Lenz EquationThe Physics I Version

Applications of EMF• Inductors• Speakers/Microphones• Electric Generators*• Electric Motors• Transformers

*Most EMF generators (like the kind that produce the electric power in your home) produce an Alternating Current.

Faraday’s (Lenz’s) Law• Any change in the magnetic environment of a

coil of wire will cause a voltage (emf) to be "induced" in the coil. No matter how the change is produced, the voltage will be generated.

• As a result of this induced voltage (emf: electro-motive force), there is an induced current in the coil producing a B-field to offset any change in the B-field already present.

• Faraday’s Law is written mathematically as:

inducedemf Nt

The negative sign actually comes from Lenz’s Law, which postulates that the current produced resists the change in magnetic flux.

Galvanometers and induced current.

• Changing the magnetic field around a wire, especially a coiled wire produces a counter current in the wire or coil. This current is in the reverse direction of the forced current flow in the wire and occurs naturally as nature’s offsetting response to a change in magnetic flux (the amount of magnetic field flowing around the wire).

• A galvanometer is a special type of ammeter designed to measure this “induced” or changing current.

• Induced currents can be created even in a coiled wire that is not part of a larger circuit.

Loudspeakers• An application of the magnetic force on a

current carrying wire is a loudspeaker. In order to understand how a loudspeaker works, one must first examine a device known as an inductor.

• A microphone is the reverse of a speaker.

Inductors and Inductance• An inductor is a solenoid inserted into an

electric circuit designed to slow the growth of current flowing in the circuit by producing a reverse current. This occurs according to Faraday’s (Lenz’s) Law.

• http://www.ngsir.netfirms.com/englishhtm/RL.htm

• Notice the reverse current that slows the build of forward current in the circuit when the switch is closed.

Switch is open, circuit is off

Switch is closed (current flows from battery)

Switch closed a long time…

So when an inductor is in place, the amount of current flowing in the circuit depends on time!

In this case, after the circuit has been operating for a long time, the current has stabilized at a maximum and the inductor simply functions as a wire, or short circuit.

Speakers• A speaker is a special type of inductor.• A sound wave can be stored as an electrical signal.

Basically the pattern of increasing and decreasing sound waves is saved as a corresponding increasing and decreasing voltage/current. This electric signal is amplified many times and sent to the speaker. As the current to the speaker changes, the current in the speaker/inductor changes. There is a corresponding change in the B-field. This change in B-field produces a force which causes the inductor to vibrate against the cone of the speaker. This vibration is picked up by the air around the speaker and eventually by your ears.

What it looks like…

http://electronics.howstuffworks.com/speaker6.htm

Speakers and Microphones• A speaker produces mechanical vibrations (sound)

when the changing current in an inductor produces a variable force on the wire. Thus, a speaker converts an electrical signal (waveform) to a mechanical wave.

• A microphone converts a mechanical wave, like sound, to an electrical signal.– That signal can be stored, or saved, in many forms as

an electronic media file, either in computer memory (on a re-writable “hard disk” or RAM), or on some sort of physical data storage device (magnetic tape like floppy disks, cassettes, VCR tapes, or other device like vinyl records, CD’s, DVD’s etc…)

– All these devices are a medium for saving a sample of, or for reproducing an electric signal that can be converted into sound.

Electric Motors• We know that currents in B-field experience

a force due to the magnetic field’s effect on the moving charges in the current.

What will be the direction of current in the loop?

Recall:EMF = BLvSo, when v=0, EMF=0

Start the motor. v 0, EMF = #, current flows in the loop.

If we have current, we have a force on the wire.Fon a wire = iLB

As the motor turns, a switching circuit can be used to keep the direction of current flow constant relative to the space.

Generators

• An electric generator is a device that provides a voltage source by means of an induced EMF.

• In a simple generator, a loop of wire turns in a magnetic field. The turning is usually provided by some mechanical process (steam rising, or water falling). The B-field induces a current in the wire that can be used in a circuit to do work.

EMF = BLvIn a generator, v is maximized perpendicular to the field when the sides of the loop are in line with the source of the magnetic field. Since B and L would both be constant, this condition would maximize the output EMF and the output current. Current and voltage output both follow a sine wave.

Improvements• Electric motors and generators are both

applications of the same physical principles.

• We use generators to produce a strong EMF or voltage that we can harness for electricity. We use motors to do mechanical work. The induced EMF in a motor is an added bonus. The alternator in your car is basically a generator driven by you’re the turning of your car’s motor.*

*The motor in your car is actually a thermodynamic “heat engine,” using the heat from combustion to do mechanical work. This is not the same as an electric motor! Although, the end result (mechanical work) is the same in both cases.

Questions:

• Are there ways that we can increase the output of motors and generators?

• What variables can we change to increase the output?– Hint: Think about physical changes we can

make to the systems.

Direct Current

• Batteries produce a steady potential difference (high vs. ground) and with the exception of time dependent components in a circuit (like capacitors and inductors), the current flow in a circuit powered by a battery is constant. We call this Direct Current or DC.

• Generators can be designed to produce a direct current if a switch is employed (like a motor)

Alternating Current

• We have already seen how an “alternating current” or AC generator works. An electric voltage source that is oscillating produces current that varies with time.

• The type of current produced by an AC generator is analogous to creating a simple DC circuit with a battery, then flipping the battery over again and again. Sort of…

• Basically, this type of system produces current that flows in one direction for a short amount of time and then reverses to flow in the opposite direction. Since most appliances either don’t “care” or are designed to operate in this type of environment, everybody wins!

• In the U.S. and many other countries, electric generators are standardized to produce an average frequency at 60 Hz, that is to say they reverse 60 times each second.

• Likewise, the voltage pumped into your home is standardized between 110V and 120V. Most of your appliances (except your dryer) are designed to operate on an AC power supply of 120V at 60Hz.

AC vs. DC• In the late 1800’s (c. 1880) the race was on that would

determine the course of electric power generation to the present day.

• The vision of Edison’s General Electric company was to provide DC electric power to consumers in cities. His idea was that each city block would have its own power station.

• In 1893 at the Chicago World’s Fair, N.Tesla powered (lit) the entire fair with electricity transmitted all the way from his hydroelectric plant on Niagara Falls.

• Edison fought back with a public campaign of misinformation, going so far as to blow up cattle in a display of the “danger of alternating current.” Of course, you could achieve the same result with DC current too, but Edison didn’t tell anybody that.

AC Advantages• Since you are only pushing current in any one direction

for a very short amount of time (1/60th of a second) AC power generation is highly advantageous as it allows you to provide a very high voltage, low current signal that can be transmitted, hundreds, or potentially, thousands of miles.

• The single disadvantage to AC power is that circuits must be designed to operate in an environment where the voltage was constantly changing. In the modern era, this disadvantage is no longer a large problem since, while AC circuits are slightly more complex than a DC circuit designed for the same function, we now have 100+ years of experience behind us in designing circuits.

• In addition, we now have portable transformers (those heavy little black boxes that some of your appliances use as plugs) that will convert a 120V, 60 Hz AC signal to a DC signal for use in some appliances.

Transformers• A transformer is a device that uses B-fields

and induced currents to create and exchange between current and voltage.

• For example, let’s say you have a 120V input line but only require 6V to operate a certain appliance. If you were to hook up the appliance directly to the 120V source, what do you suppose would happen?

• Therefore, we need something to “step-down” the voltage of our input line before it gets to the device.

• Transformers are analogous to a system of locks on a river or canal. They allow you to step down the input voltage, but with a trade off. As the voltage is decreased, the current output of the transformer increases.

• A transformer is basically a core made of soft iron formed into a hollow square. On one side of the core the input wire comes in and wraps around the core forming a solenoid. When current flows, a magnetic field is created in the iron core. This B-field induces a current in the output wire, which is formed into a solenoid around the other side.

“Step up” vs. “Step down”• Some transformers increase voltage at the

expense of current. This is a step up transformer. Step-up transformers have fewer coils in the input solenoid and more coils on the output side of the core.

• A step down transformer (like those at power switching stations, the grey cylinders on phone poles, the green boxes in yards and the little black “plug boxes” you use at home sometimes) increases current at the expense of a decreased voltage. These transformers have many more coils on the input side of the core.

Also see This Linkhttp://www.osha.gov/SLTC/etools/electric_power/illustrated_glossary/substation_equipment/power_transformers.html

Questions:• A wire 20.0 m long moves at 4.0 m/s perpendicularly

through a magnetic field. An EMF of 40 V is induced in the wire. What is the strength of the magnetic field?

• A straight wire, 0.75 m long moves upward through a horizontal 0.30T magnetic field at a speed of 16 m/s. What is the EMF induced in the wire?

• A hair dryer uses 10 A at 120 V. It is used with a transformer in England where the line voltage is 240 V.

A) What should be the ratio of the number of turns in the transformer?

B) What current will the hair dryer now draw?