Introduction to Electromagnetism

“If, in some cataclysm, all of scientific knowledge were to be destroyed, and only one sentence passed on to the next generations of creatures, what statement would contain the most information in the fewest words? I believe it is the atomic hypothesis (or the atomic fact, or whatever you wish to call it) that all things are made of atoms—little particles that move around in perpetual motion, attracting each other when they are a little distance apart, but repelling upon being squeezed into one another. In that one sentence, you will see, there is an enormous amount of information about the world, if just a little imagination and thinking are applied... “

-Richard Feynman, Six Easy Pieces

The atom, the basic building block of everything we experience in our day-to-day lives, consists of only three pieces. The nucleus, or central core, consists of two types of particles, the positively charge proton and the uncharged (or neutrally charged) neutron. Orbiting the nucleus are the negatively charged electrons

Figure 1 - Simple model of Lithium Atom (http://en.wikipedia.org/wiki/Chemistry#mediaviewer/File:Atom_diagram.png)

The positive charge of the protons attracts the negatively charged electrons and keeps them tightly bound to the atom. Almost all properties of matter (color, hardness, texture, smell, freezing and boiling, etc.) are based on the electrons surrounding the nucleus.

There are only four different types of forces discovered, the nuclear strong force, the nuclear weak force, the electromagnetic force, and the gravitational force. The electromagnetic force has the greatest impact on our day-to-day lives. It is responsible for all interactions between atoms and it is the reason we see, feel, taste, and smell objects. Without it there would be no solids or liquids for us to experience. But one question that is rarely addressed is why are electricity and magnetism lumped together into a single force. Aren’t they two different things? Magnets don’t seem to attract charged particles and magnets don’t seem to react to electric fields. It turns out there is a very strong, very fundamental tie between the two types of interactions and the two interactions would be almost indistinguishable if not for one very surprising fact: no one has ever seen the magnetic equivalent of a lone electric charge; we have yet to discover a magnetic monopole.

The goal of these activities will be to explore how we know individual electric charges exist (charges are also called electric monopoles), how we can discover that magnets have two different types (or poles), and how electric charges give rise to magnetism in magnetic materials.

Introduction to Electric Charges(activity adapted from Matter and Interaction, 3rd Edition by Chabay and Sherwood)

Materials Needed: A roll of Scotch Magic Tape™ (or similar brand) Pen or pencil Paper

Preparations:1. Pull off six strips of tape about 10 cm long (4 inches) and fold over one end of

each piece to form a handle.2. Place two pieces on a smooth surface such as a table or piece of plastic and

smooth them down. You will be using these two pieces as your base and will leave them in place for the entire experiment.

3. Place another piece of tape on top of the base pieces. Write “B” (for Bottom) on each of these pieces of tape.

4. Place your last two pieces of tape on top of the bottom pieces. Write “T” (for Top) on each of these pieces.

5. Pull the T and B pieces of tape off of the base together (do not separate the T and B tapes just yet) and stick one end of the B tape to the side of the table so it is hanging down.

6. Notice that if you bring your hand near the hanging tape that the tapes will be attracted to your hand. Try rubbing your hand along the smooth side (not the sticky side) of the tape a few times until the tape is no longer attracted to your hand.

7. Grab the handles of the T and B tape and slowly pull only one of the T tapes off and stick it to the side of the table several inches away from where the B tape is stuck to the table. We will call this the hanging T tape.

Experiments:1. Try bringing different types of objects near the T tape and see what types of

things can attract the T tape. Examples include your hand, books, pencils, paper. List which things attract the T tape and which ones don’t affect the T tape.

Attract T Tape Don’t Attract T Tape

2. Based on what you have seen so far, what do you think will happen when you pull the other T tape off of the L tape and bring it close to the hanging T tape? Do you think the two pieces of T tape will be attracted, not attracted, or something else?

3. Pull the second T tape off of the L tape by the handle and bring it close to the other hanging T tape. Describe what happens.

4. Did the experiment agree with your prediction?

5. What do you think will happen if you take one of the L tapes and bring it close to the other hanging L tape? Do you think they will be attracted, repelled, or do you think nothing will happen? Explain what information you are basing your prediction on.

6. Go ahead and take one of the L tapes and bring it near the other L tape. Describe what happens.

7. Was your prediction about what happened to the two L tapes correct?

8. What do you think will happen if you bring an L tape near the hanging T tape? Make a prediction before you actually try this. Explain what information you are using to come up with your prediction.

9. Move the L tape near the hanging T tape and describe what you see.

10. Was your prediction correct?

11. Summarize your results in the table below, stating whether each pair of pieces of tape will repel or attract:

Experiment ResultTwo B tapes will:Two T tapes willA T tape and B tape will:

Using only two different types of charge (T and B) we can describe all of the above experiments. What would we expect to see in our experiments if there was a third type of charge (let’s call it O for Other)?

12. Imagine you have a third piece of tape with unknown charge and you see that it is attracted to B tapes but repels T tapes. Would you conclude that this has charge T, charge B, or charge O?

13. Another piece of tape is brought near hanging pieces of tape and is found to attract the T tape but repel the B tape. Would you say this unknown piece of tape has charge T, charge B, or charge O?

14. A different piece of tape is brought near the hanging tape and is found to attract both the T and B pieces, but when another identical piece of tape is brought near the original, they both repel one another. Would you say the unknown pieces of tape have charge T, charge B, or charge O? Give an explanation of what you are basing your decision on.

By now you’ve probably noticed that both the T and B tapes are attracted to your hand. How does this happen and is this an indication of a third type of charge? To answer this question, tear off two pieces of paper about as wide the tape and roughly 10 cm long.

15. What do you expect will happen when you bring the paper strips near the T and B pieces of tape? Do you think the paper will be attracted to both, repel both, or be attracted to one but repelled by the other?

16. Try the experiment and see what happens. Describe your results below.

17. If both pieces of paper have a third type of charge, what would you expect to happen when you bring the paper close to each other? Would you expect them to attract, repel, or do nothing?

18. Bring the strips of paper together and describe what happened.

The two strips of paper should not have been attracted or repelled from each other (if they did, it was probably because they touched one of the charged pieces of tape. Try the experiment over but make sure the paper never touches the tape). The pieces of paper don’t interact with each other because they are both neutrally charged, that is they have the same number of T and B charges. However, when the paper is brought near a T charged tape, the T charges in the paper move a little away from the T tape and the B charges move a little closer. Since the B charges are closer, the paper is attracted to the tape. This process where the two types of charges in a neutrally charged object shift around to become attracted to another charged object is called polarizability and we say that the paper became polarized.

Summary:Based on a few simple experiments involving pieces of tape you have determined that there are at least two different types of electric charge. You also saw that similar charges repel each other and opposite charges attract each other. Neutrally charged objects that have an equal number of each type of charge can be attracted to charged objects by becoming polarized.

Although we cannot conclusively prove that there is no third type of charge, no experiments have ever shown there to be a third type. Additionally, all established physics theories require only two types of charges.

Additional Activities:You can explore how the electric forces vary with distance, as well as how to charge up other objects such as balloons, combs, or plastic rods. This will open up a whole area of exploration called triboelectricity. A good resource for other fun

electrostatic activities is http://www.arborsci.com/cool/part-1-electricity-all-charged-up.

Electric Force, Fields and the Electric Monopole

Materials Needed: A roll of Scotch Magic Tape™ (or similar brand) Pen or pencil Paper

Preparations:1. Create two T (Top) charged tapes, one about 5 cm long and the other one 10

cm long. You will also need a 10 cm long B (Bottom) charged tape.2. Take another piece of tape and fold it in the middle so it forms a ‘T’ with the

sticky side on the top of the ‘T’. 3. Place the ‘T’ in the middle of a blank sheet of paper. The leg of the ‘T’ should

be sticking straight up. Rub your finger along it to make sure it is not charged.

4. Attach the shorter of the charged tape pieces to the leg of the ‘T’ in the middle of the blank page. This piece of tape will be our stationary charge.

Experiments:1. You will use the longer piece of charged tape (which will call our detector

charge) to map out the forces exerted by the stationary charge. Move the charge around the stationary charge and at 2 cm intervals draw an arrow indicating the direction of the force exerted on the detector charge by the stationary charge. Draw a longer arrow for larger forces.

2. What do you notice about the direction the arrows are pointing?

3. What do you notice about the size of the arrows (magnitude of the force) as you get closer to the stationary charge?

4. Pick on of the arrows you drew. If you took another T-charged tape that had even more charge on it and placed it near the arrow, which way would the force be on the new tape? In the same direction as the arrow, opposite the direction of the arrow, or in some other direction?

5. Pick one of the arrows you drew. If you placed a B charged tape at that point, which way would the force on the B charged tape by the stationary charge be? Would it be in the same direction, the opposite direction, or some other direction?

6. Try bringing the B charged tape near where your arrow is drawn and see if your prediction was correct. Where you correct?

Summary:What you have drawn represents the electric field of the stationary charge. It is called a ‘field’ because it exists at every point in space near the stationary charge, even at points where you didn’t draw any arrows. This field tells us about how other charges would interact with the stationary charge. Any piece of tape with the same charge as our detector charge will be pushed in the direction of the arrows while an oppositely charged piece will be pushed in the opposite direction.Notice that all of the arrows point away from the stationary charge. None of the arrows change direction or switch back towards the stationary charge. This tells us that the stationary charge only has one type of charge on it. We call an object with only one type of charge a monopole. An electron or proton is an example of a monopole.

7. If you used an electron as the stationary charge and a proton as the detector charge, what would the field lines around the electron look like? (Note that the convention is to use positive charges as detector charges so electric field lines always point towards negative charges and away from positive charges)

Additional Activities:See the PhET website for good activities exploring electric fields

https://phet.colorado.edu/en/simulation/charges-and-fields https://phet.colorado.edu/en/simulation/electric-hockey https://phet.colorado.edu/en/simulation/efield

Magnetic Poles and Fields

Materials Needed: Two bar magnets A magnetic compass Pen or pencil Paper

Experiments:1. Your first goal is to figure out how many different types of magnetic poles

there are. This is similar to the experiment you did with the pieces of tape where you determined there were only two kinds of electric charge. Try bringing the ends of the magnets together and write down whether the two ends repel or attract.Experiment ResultTwo N ends will:Two S ends will:An N and an S end will:

2. Based on your results above, how many different types of magnetic poles are needed to explain your results?

3. Which of the following scenarios would indicate that a third type of magnetic pole (let’s call it W) exists?

Scenario 1Experiment ResultW and N will: AttractW and S will AttractTwo W ends will: Attract

Scenario 2Experiment ResultW and N will: AttractW and S will RepelTwo W ends will: Attract

Scenario 3Experiment ResultW and N will: Repel

W and S will RepelTwo W ends will: Attract

Scenario 4Experiment ResultW and N will: AttractW and S will AttractTwo W ends will: Repel

Describe how you chose which scenarios indicated a third type of pole.

It turns out that not only have scientists never seen a W pole, none of the physics theories require more than two types of poles.

4. Imagine that you have a N monopole (i.e. no S pole – we’ll see why this is a problem shortly) as a stationary pole in the middle of the page and you are using a second N monopole as your detector. Draw the direction of the force exerted on the detector pole by the stationary pole at several points in the space below.

N

5. How would the filed lines change if you used a S pole for your stationary pole? Note that convention is that the detector pole is always a N pole.

6. Place one of the bar magnets in the middle of a piece of blank paper. Use the N end of the magnetic compass as a detector to determine the direction of the force exerted on the detector by the stationary pole (NOTE: The magnetic N pole of the compass is actually labeled South on the compass). Draw arrows every 5 cm or so to get a good description of the magnetic field.

7. How does the magnetic field of the bar magnet differ from the magnetic field of a monopole (or the electric field of your piece of tape from an earlier activity)?

8. Do the arrows point towards the N pole or S pole of the bar magnet?

The magnetic field represented by your arrows is called a dipole field or the magnetic field of a dipole because it has two different types of poles. The field arrows point towards one end of the magnet and away from the opposite end. All dipole fields will have a similar shape.

9. Imagine that you broke your bar magnet in half right at the middle between the N and S pole. What do you think the magnetic field would look like for the N half of the magnet? Sketch the field below.

If you thought the N half of the magnet would look like a monopole you are, surprisingly, wrong. What you would end up with is two smaller magnets with a N and S end. You could keep on breaking the magnets in half but you would always end up with a dipole. In fact, when you got down to a single atom you would find that the magnetic field was still a dipole.

To date, no one has found a magnetic monopole, a single N pole or single S pole all alone. Scientists have created objects that behave like N or S poles, but they are nothing more than really long, flexible magnets with a N end and S end that move independently of one another. Theories do predict the existence of the magnetic monopole but they still remain undiscovered by us.

Additional Activities:What is magnetic? Have students explore what types of materials are attracted to magnets and see if they can determine what properties they have in common.You can also explore some of the magnetic activities on the PhET website:

https://phet.colorado.edu/en/simulation/magnets-and-electromagnets https://phet.colorado.edu/en/simulation/magnet-and-compass

N

Electricity and Magnetism Together

There are only four types of forces known to scientists and all other forces are caused by these fundamental forces:

Nuclear Strong Force Nuclear Weak Force Electromagnetic Force Gravitational Force

But magnetism and electricity seem to be two different things so why are they combined into a single force? The goal of this activity to try and answer that question.

Materials Needed: A roll of Scotch Magic Tape™ (or similar brand) A bar magnet

Preparations:1. Create a T-charged piece of tape and a B-charged piece of tape, each about 5

cm long.

Experiments:1. Try bringing the T-charged and B-charged pieces of tape near the N and S

poles of the magnet. Record whether each tape is repelled or attracted to the magnetic pole.Experiment ResultT tape and N pole will:T tape and S pole will:B tape and N pole will:B tape and S pole will:

2. Try bringing both the T and B tapes near another object like your hand or the table. Does the tape behave any differently around the N or S poles than it does near a non-magnetic object?

3. Based on your observations, does a magnetic field have any effect on a charged piece of tape?

It turns out that in order to see any effects, either the magnet or the charged particles need to be moving. If the magnet and charged particles aren’t moving then they don’t have any impact on each other.

Moving Charges4. When a wire is hooked up to a batter or a voltage supply the negatively

charged electron start moving in the wire. Your instructor will demonstrate this for you.

5. What does the magnetic field around the wire look like when the electrons are moving through the wire? Sketch the force arrows in the space below.

6. What effect did turning the power on have on the charged pieces of tape?

7. When your instructor changes the direction that the electrons move, how do the force arrows change? Describe the change in the direction of the field lines.

Wire coming out of page

8. The electrons are moving along the length of the wire. What can you conclude about the direction of the magnetic field caused by the moving charges relative to the direction the charges are moving? Are the magnetic forces in the same direction as the motion of the charges or perpendicular to the direction the charges are moving?

From this experiment we can conclude that a moving electric charge behaves like a magnet and creates a magnetic field. This is the first glimpse of an explanation why electricity and magnetism are tied together as a single force. It is also at the heart of how magnetic materials become magnetic.

Moving MagnetsYour instructor will demonstrate what happens when you push or pull a magnet through the center of a coil of wires. A current is detected when the magnet moves, indicating that there are electric charges moving.

9. Based on the fact that stationary electric charges aren’t affected by magnetic fields, what can you conclude a moving magnet causes? Hint: A moving electric monopole creates a magnetic field so…

10. Does the speed with which the magnet is moved affect how quickly the charges in the coil move (more current means faster charges typically)?

11. What happens if the magnet is moved towards the side of the coils rather than through the center? Do you see evidence of charges moving?

12. Based on your experience with the magnetic field created by a moving charge, what do you think the electric field generated by the moving magnet looks like?

Additional ActivitiesOnce again the PhET website has a plethora of simulations and activities:

https://phet.colorado.edu/en/simulation/magnets-and-electromagnets https://phet.colorado.edu/en/simulation/generator https://phet.colorado.edu/en/simulation/faraday

Origins of MagnetismYou’ve learned quite a bit about electric charges and magnetic poles so far. You know that:

Like charges repel, opposite charges attract. Like poles repel, opposite poles attract. No one has found a magnetic monopole yet so magnetic poles always come as

pairs. Stationary magnets and stationary charges don’t interact. A moving electric charge creates a magnetic field A moving magnet creates an electric field.

If no one has found magnetic monopoles then where does magnetic material come from? Each electron behaves like it is spinning and as you now know, a moving charge creates a magnetic field. The field of a rotating sphere is similar to a current loop.

Figure 2 Magnetic field caused by electric current loop - From http://en.wikipedia.org/wiki/Magnetic_dipole#mediaviewer/File:Magnetic_field_due_to_current.svg

The magnetic field formed is a perfect dipole, like a bar magnet shrunk small. In most atoms each electron is paired up with another electron spinning in the opposite direction, with a magnetic dipole pointing in the opposite direction. These two paired electrons cancel each others magnetic fields. This means that only atoms that have unpaired electrons will behave like magnets.

If you apply a magnetic field to one of these materials with unpaired spins you will frequently see the material behave like a magnet itself. A good example is if you pick up a paper clip with a magnet, the paper clip itself is now magnetic. However, once you remove the magnet from the paper clip it quickly loses its magnetism. How does it become magnetic and why does it lose it?Neighboring atoms in magnetic materials like to line up together and form domains, kind of like neighborhoods of magnetic fields all pointing in the same direction. However neighboring domains may point in different directions. If you bring a magnet close to this material all the domains will line up, making the material magnetic.

Figure 3 Arrows represent magnetic field of atoms - Image from http://en.wikipedia.org/wiki/Magnetic_domain#mediaviewer/File:Dominios.png

Once you remove the magnet from near the paper clip, the random thermal motion of the atoms causes them to change direction and mixes up the directions of the atoms.Additionally, it takes energy to create a magnetic field, so if possible a magnetic material would rather have all of its magnetic fields cancel out

Figure 4 Creation of domains to cancel out magnetic fields - From http://en.wikipedia.org/wiki/Magnetic_domain#mediaviewer/File:Powstawanie_domen_by_Zureks.png

So the next question you might ask is, if magnetic materials want to cancel out their magnetic fields, why do magnetic domains form at all? Why don’t all the magnets just line up N to S and S to N, canceling magnetism all together? The key is something called the exchange interaction, which is a little bit strange but it is also an incredibly powerful concept.

The Exchange InteractionRemember when I said there are only four fundamental forces? Well, there are still only four, and the exchange interaction isn’t one of them. It isn’t even a force at all, but it behaves like there is a force. It turns out it is a statistical result imposed by quantum mechanics (which is where all the fun physics resides).All electrons are identical. You cannot tell any two electrons apart. In fact, the physicist John Wheeler proposed that there is really only one electron in the whole universe. One strange requirement of quantum mechanics is that the function that controls how electrons move must change signs if you were to exchange any pair of electrons (we say the function describing the electrons must be antisymmetric so that f(electron1, electron2) = - f(electron2, electron1)). One result of this exchange rule is that if two electrons are in the same orbital they must have opposite spins. You may know this as the Pauli Exclusion Principle and it is responsible for the shell structure of electrons in various atoms. If the electrons are not in the same orbits but are near each other the exchange rules require that the spins of the electrons line up and so does the magnetic fields. If two neighboring atoms get too far apart then the exchange rules no longer are needed and the magnetic fields are no longer aligned. It is only in certain materials like iron, platinum, cobalt, and a few others that the distance between the outermost electrons in neighboring atoms are at just the right distance from each other so that the exchange rule requires the electrons to line up. A whole chain of these atoms can come together to form a magnetic domain.Hopefully your next question is why does the exchange rule place these requirements on the function that describes how electrons move. To answer that you will need a bit more quantum mechanics, but at some point you just have to tell students that it’s turtles all the way down.1

1 This is from Stephen Hawkings A Brief History of Time. The quote goes “A well-known scientist (some say it was Bertrand Russell) once gave a public lecture on astronomy. He described how the earth orbits around the sun and how the sun, in turn, orbits around the center of a vast collection of stars called our galaxy. At the end of the lecture, a little old lady at the back of the room got up and said: "What you have told us is rubbish. The world is really a flat plate supported on the back of a giant tortoise." The scientist gave a superior smile before replying, "What is the tortoise standing on?" "You're very clever, young man, very clever," said the old lady. "But it's tortoises all the way down!"”

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