Lecture 8-1

Magnetism (Chapter 24)

MAGNETIC Poles, Forces and Fields DEMO magnet and paper clips (Comment on the weakness of the gravitational field)

Similar to the arguments I gave back when we introduced the causes of all electrical phenomena, I will repeat this for the magnetic phenomena. 1. What is the cause of all magnetic phenomena? A moving electric charge.

However, magnetism was first believed to be cause by magnetic poles. There are two types of magnetic poles: North and South magnetic poles.

2. Since there are two types of magnetic poles, there are two types of magnetic forces: attractive or repulsive

DEMO domain model and two magnets

3. The magnetic force is transmitted through the magnetic field (defined as B-field).

4. Biot-Savart law (inverse square law): The farther two magnets get from each other, the weaker the magnetic force between it is.

2B1

(distance)F ∝

Units of measurement: Gauss or Tesla

The B-field direction is measured using a compass.

DEMO Compass and magnet

Earth’s Geomagnetic Field The earth behaves magnetically almost as if a bar magnet were located near its center. The axis of this fictitious bar magnet does not coincide with the earth’s rotational axis but is currently tilted about 11o from the Earth’s rotational axis.

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What is the cause of the earth’s magnetic field? However, unlike the field of a bar magnet, Earth's field changes over time because it is generated by the motion of molten iron alloys in the Earth's outer core (the geodynamo). A cutaway artwork of the earth illustrating the convection within its interior and the pattern of its magnetic field.

• The Earth has a solid center (inner core, blue), which is surrounded by a liquid layer (the outer core, yellow) where molten iron circulates (red arrows). The outer core is surrounded by the mantle (red). The core rotates faster than the bulk of the planet which means that the inner core gains a full turn on the rest of the planet every 400 years.

• The convective motion of molten iron in the outer core combined with the Earth's rotation is what produces the dipole magnetic field (blue arrows). That is, the magnetic field is thought to be generated by the spiral movement of molten iron in the Earth's liquid outer core (yellow), which acts as an electromagnet.

There are two key points about the geomagnetic field: 1. The Magnetic North Pole wanders, fortunately slowly enough that the compass is

useful for navigation. At random intervals (averaging several hundred thousand years) the Earth's field reverses (the north and south geomagnetic poles change places with each other). These reversals leave a record in rocks that allow

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paleomagnetists to calculate past motions of continents and ocean floors as a result of plate tectonics. • The magnetic pole moves from one pole to the other slowly over the years. For

example, it current location is about 770 km northwest of its position in 1904. There has been a 5% decrease in the earth’s magnetic field over the past 100 years. If this steady decrease would continue, in 2000 years the earth’s magnetic field would be “zero.”

• The magnetic pole of the earth has been known to reverse directions. In fact, there have been 20 reversals in 5 million years. Most recent reversal was 700,000 years ago, than, 870,000 years, then 950,000 years.

2. The region above the ionosphere, and extending several tens of thousands of kilometers into space, is called the magnetosphere. This region protects the Earth from cosmic rays that would strip away the upper atmosphere, including the ozone layer that protects the earth from harmful ultraviolet radiation. More on this later on.

The earth’s magnetic field plays a role in the way honeybees (as well as pigeons) navigate between their hive and the flowers they visit. Magnetic Domains and Creating a B-field A bar magnet has two poles. If one breaks a bar magnet to isolate the North and South Pole, one will instead find that the bar magnet has now become two magnets. If I continue to break the magnet into smaller and smaller pieces, eventually I will get to the atomic level and find that the real reason why the bar magnet had a B-field was that the electrons where circling the nucleus. Because the electrons can either rotate either Counterclockwise (CCW) or Clockwise (CW), we can determine the direction of the rotations in term of “spin” by using the Right-hand Rule. If my fingers/hand encircles the motion of the electrons in the CCW direction, my thumb points upward. This thumb direction represents the spinning motion of the electrons and is called spin-up. However, if I repeat this process for the CW motion, I have to rotate my fingers/hand upside-down so that my thumb now points downwards; this is called spin-down.

When there is a collection of atoms with the same spin orientation, they these atoms form a magnetic domain (a little neighborhood of similar spinning atoms). Depending on whether the magnetic domains are align or not, then a magnetic field is produced. That is,

What is the difference between a strong (Neodymium) and weak (cow) magnet?

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MAGNETIC DOMAINS – Induced Magnetism Analogy: electric polarization occurs with a charged balloon polarizing the atoms in the wall (i.e., it causes the atoms to rearrange their charge distribution), and results in the balloon sticking to the wall.

So how do the refrigerator magnets work? Before the magnet is placed on the refrigerator, the domains are randomly arranged (unmagnetized). When the magnet is brought to the refrigerator, the magnet induces magnetization: similar to electric polarization, the magnetic domains rearrange themselves so that the surface of the refrigerator is magnetized to be magnetically north. As a result, the magnet sticks to the refrigerator.

Example: why does a magnet pick-up several paper clips?

DEMO magnet and paper clips

Applications of domains: 1. Magnetic strips on credit cards

DEMO domain model and magnet

2. MRI domains

Electric Currents and Magnetic Fields If a moving charge produces a B-field, then electric current will also produce a B-field.

smaller current smaller B-field produced

B-field currentlarger current larger B-field produced

→∝ → →

For a single current-carrying wire, the B-field encircles the wire according the Right-hand Rule. The Right-hand Rule says that if your thumb points in the direction of the current and let your fingers curl around the direction of the thumb, the B-field by this wire encircles the wire in circular paths. If we repeat this process with the solenoid, the B-field of the solenoid is very similar to a bar magnet as shown below.

Since the solenoid acts like a magnet, it can repel other magnets when similar pole magnets are inset into its core.

( ) ( ) more turns stronger B-fieldB-field of solenoid number of turns of wie current

less turns weaker B-field →

∝ → →

DEMO Solenoid and compass on overhead; eject magnets; Domain model with coil

If you look at this magnetic launcher, note that it has a solenoid coil. So when I turn on the voltage, a current will produce a B-field that is north pointing upwards. Without going into the details, if I place an aluminum ring around the solenoid, the solenoid will in turn produce a current in the aluminum ring such that it produces its own magnetic field that is the same B-field of the solenoid. As a result, these two fields interact and the ring is repelled upwards. See picture on the right. Here is the important detail: if you want to make a stronger B-field, it is common to insert inside the bore of the solenoid an iron core. So how does this increase the B-field field strength of the solenoid? When the magnetic

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launcher is turned on, the B-field of the solenoid will magnetize the domains of the iron core so that the B-field of the solenoid and the domains add together:

As a result, the combined B-field of the two are much stronger and the ring will not be launcher up much higher as before.

DEMO Magnetic launcher, ring, iron core

Application: How does a speaker work?

Faraday’s Law and Electrical Power Generation Faraday’s law is the key concept that is used to generate more than 95% of all electrical power in the world. From the diagram below, only a small amount of the Other Renewable energies (mainly solar power) does not use Faraday’s law.

Let’s go back to the magnetic ring launcher again to explain Faraday’s law in detail. As we have already stated, a current produces a B-field:

producescurrents B-field→ Faraday’s Law essentially tells us how one can reverse this process, that is, how one can start with a magnetic field and produce a current. Faraday Law Any change in the magnetic environment of a coil of wire will cause a voltage to be "induced" in the coil. No matter how the change is produced, the voltage will be generated. The change could be produced by changing the magnetic field strength, moving a magnet toward or away from the coil, moving the coil into or out of the magnetic field, rotating the coil relative to the magnet, etc. To be more specific, a time-varying B-field will produce a time-varying voltage (or current):

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produces

time-varying currenttime-varying B-field time-varying voltage→

PhET Applet Faraday’s Law (choose pickup coil): http://phet.colorado.edu/en/simulation/faraday

DEMO Galvanometer, coil, magnet

Key points: • If the magnet is moving towards (or away) from the coil, a voltage/current is induced

in the coil as read by the galvanometer’s needle moving. • If the magnet is stationary, there is no voltage/current in the coil since the

galvanometer has no reading. • Only changes time-varying changes in the B-field strength inside the bore of the coil

will produce a voltage/current in the coil. Power Plants Where do we get the electrical power for our homes and industries? These are generated at power plants. There are many different kinds of power plants but the basic structure is roughly the same. Consider the following diagram

This is a diagram of the workings of a boiling water reactor (BWR). In a BWR, the core (yellow columns) is suspended in water (blue). The heat produced by the nuclear reactions boils the water into steam (red). This turns a turbine (green), which drives an electricity generator (grey). The steam then passes through a condenser, which uses water from a cooling pond (lower right), before being passed back into the reactor chamber. The water acts as both the reactor coolant and the moderator. Control rods (blue, between core columns) can be raised or lowered to control the reaction. This is a cheap and simple reactor.

Electrical generator core (coil) Only the outer part of the core is seen here, consisting of numerous electrical wires arranged around the central space. When in use, a turbine (not seen) will drive a shaft that runs through the central space. Magnets on the shaft will rotate as the shaft rotates, inducing electrical currents in the wires. This electrical current is then distributed around a grid and used to power electrical devices. The rotation of the turbine is usually by steam in a coal or nuclear power station, but other types of power include wind, geothermal, and hydroelectric power.

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PhET Applet Faraday’s Law (choose generator): http://phet.colorado.edu/en/simulation/faraday

Hydroelectric Power Hoover Dam on the Colorado River and a Prototype wave-powered electricity generator in Scotland (supply electricity to small, isolated communities).

Wind Power

Heat Power: Odeillo-Font-Romeau solar power station in the Eastern Pyrenees, France

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Positioned in front of the reflector is an array of 63 flat orientating mirrors that automatically track the motion of the sun. The reflector is composed of 9,500 mirrors which concentrate the sun's rays onto a dark-coated furnace at its focus (central tower). This system is capable of achieving a temperature of 3,800oC.

Sewage Power (England)

Generators obtain electricity from burning methane gas produced from sewage (England).

Smog Power (Proposed tower design to remove smog from air whilst making power)

The tower is made from steel columns (red) with Teflon-coated fiberglass (white) stretched between them. It is up to 60 stories high & 150 m wide. A mist of charged water droplets is sprayed into the top of the tower. These droplets attract & absorb smoke particles via charge attraction. Some of the droplets evaporate; cooling the air and making it sink into the tower. As the air exits at the bottom of the tower it passes through wind turbines; these generate more electricity than is needed to pump the water up the tower. Magnetic Force on a moving charge particle There are two types of forces in nature: (i) forces that change the speed of the particle but not its direction, while the (ii) second kind of force changes the direction of the particle but not its speed. Magnetic forces are the second kind of force: they change the direction of a charge particle but not its speed. That is, magnetic forces cause electrically charged particles to turn in circles.

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Magnetic forces are the second kind of force: they change the direction of a charge particle but not its speed. That is, magnetic forces cause electrically charged particles to turn in circles. The equation that for the magnetic force is complicated enough for me not to go into details; however, there are two things to note for our purposes. The magnetic force depends on the velocity of the charge particle as well as it direction.

Velocity dependence

B

B

a stationary charge (v 0) feels no B-force F 0a moving charge (v 0) does feels a B-force F 0

= → =

≠ → ≠

Direction dependence If a charged particle is moving parallel or antiparallel to a magnetic field, there is no B-force (no deflection force) acting on the charge particle.

If a charged particle is moving perpendicular to a magnetic field, there is a maximal B-force (deflection force) acting on the charge particle. When this is the case, the B-force will make this electric charge move in a circle such that it encircles the magnetic field lines.

If a charge particle enters the magnetic field at an angle, then the charge particle will have a helix trajectory.

DEMO TV with magnet

Why is the Earth’s B-field Important?

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The geomagnetic field and the van Allen Belts deflect the solar wind using a magnetic force.

The white lines represent the solar wind; the purple line is the bow shock line; and the blue lines surrounding the Earth represent its protective magnetosphere.

CME = Coronal Mass Ejection The Sun’s magnetic field and releases of plasma directly affect Earth and the rest of the solar system. Solar wind shapes the Earth’s magnetosphere and magnetic storms are illustrated here as approaching Earth. These storms, which occur frequently, can disrupt communications and navigational equipment, damage satellites, and even cause blackouts. The magnetic cloud of plasma can extend to 30 million miles wide by the time it reaches earth.

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Northern and Southern Lights It is caused by interactions between charged particles from the Sun (the solar wind) and gas atoms and molecules about 100 km above the Earth. On reaching Earth, the charged particles are drawn by Earth's magnetic field to the poles, where they collide with gas atoms and molecules, causing them to emit light.

Why aren't permanent magnets really permanent? The north pole of a compass is attracted to the north pole of the Earth, yet like poles repel. Can you resolve this apparent dilemma?