# PHYS 2212 Module 7

7: Magnetic Forces and Fields

An industrial electromagnet is capable of lifting thousands of pounds of metallic waste. (credit: modification of work by “BedfordAl”/Flickr)

For the past few modules, we have been studying electrostatic forces and fields, which are caused by electric charges at rest. These electric fields can move other free charges, such as producing a current in a circuit; however, the electrostatic forces and fields themselves come from other static charges. In this module, we see that when an electric charge moves, it generates other forces and fields. These additional forces and fields are what we commonly call magnetism.

Before we examine the origins of magnetism, we first describe what it is and how magnetic fields behave. Once we are more familiar with magnetic effects, we can explain how they arise from the behavior of atoms and molecules, and how magnetism is related to electricity. The connection between electricity and magnetism is fascinating from a theoretical point of view, but it is also immensely practical, as shown by an industrial electromagnet that can lift thousands of pounds of metal.

In PHYS 2211 and 2212 so far we’ve seen two fundamental forces of nature: gravity and electrical forces. Electrical force depends on the existence of charge — charges make E-fields, and then E-fields in turn exert forces on other charges: . There is another kind of force in nature, called magnetism.

Magnetic effects from natural magnets have been known for a long time. There are recorded observations about magnetic effects from the ancient Greeks from more than 2500 years ago. The word “Magnetism” comes from a Greek word for lodestone, which contains iron oxide. It was found in Magnesia, a district in northern Greece. Properties of lodestones are they could exert forces on similar stones and could impart this property (magnetize) to a piece of iron it touched. Small slivers of lodestone suspended with a string will always align itself in a north-south direction—it detects the earth’s magnetic field.

You’ve surely played with refrigerator magnets. They stick to some materials but not others. For example, magnets don’t stick to aluminum. Magnetism is not equal to Electricity — they are different forces!

Play with magnets a little. Some attract, and some repel. In fact, all magnets seem to have 2 “sides” or “poles”.

Once you’ve labeled the poles, you’ll notice they act like this:

Opposite poles attract and like poles repel. This is a bit like electricity, where we also had two charges: opposites attracted while likes repelled. But this is not electrical! So let’s avoid naming the magnetic “charges” + and -. Here’s another name: “N” and “S” (North and South). We’ll label one (arbitrarily) and then we can figure out all the others in the world.

Unlike electricity, you’ll never see a magnet with two N poles or two S poles. You always have something called a “dipole” magnet, because it has two (different) poles: N and S. If you break a magnet, you DON’T get one “N-only” and one “S-only” magnets, instead you simply get two smaller dipole magnets.

There is a magnetic field which (like E-fields) extends through space. It exerts a force on other magnetic objects. It’s a vector associated with every point in space.

We can use little “test magnets” to map out a magnetic field (just like the little “test charges” we used to map E-fields). For example, iron filings, or a small compass, near a magnet.

The compass can define the direction of those lines. We can draw arrows on field lines (pointing where the compass does). What we see looks rather like an electric dipole E-field pattern. Remember, opposites attract, and a compass needle’s tip is (by definition) “N”, so the compass points towards (is attracted to) the “S” pole of other magnets.

The Earth is a giant magnet. A compass points towards the geographic “North” of the planet, so the magnetic “S” pole (of the NS giant hidden magnet inside the Earth) sits up near the planet’s geographic N pole! (It’s a little strange, think about this picture until you understand the conventions.)

Some key questions to ask now:

• What makes/causes magnetic fields?
• How can we quantify the strength of magnetic fields?
• How can we quantify the effects of magnetic fields?

Lots of experiments were done (in the 1800’s) to figure out answers to these questions. For example:

1. Oersted discovered that magnetic fields are always created by currents, i.e. by moving electrical charges. So although magnetic fields and electric fields are very different, they are also related, too.
2. Magnetic fields exert forces on other currents.

So what about regular magnets? (Where’s the current in a kitchen magnet? You don’t need to buy batteries for them, right?!)

Answer: All atoms have tiny currents around them, all of the time! (Just the electrons in orbit.) But normally, atoms are randomly oriented, so there’s no net effect. Basically the magnetic fields of different atoms cancel. But if the atomic currents all line up (which happens only in unusual and special materials, like ferromagnets) then they act magnetic. This happens in, for example, iron (Fe), nickel (Ni), chromium (Cr), and not too much else.

The “rules” of magnetism we’re about to discuss cannot be derived, they are experimental facts. They look crazy, in fact, but this is how the world apparently works!

#### 7.1 Magnetism and Its Historical Discoveries

• Explain attraction and repulsion by magnets
• Describe the historical and contemporary applications of magnetism

#### 7.2 Magnetic Fields and Lines

• Define the magnetic field based on a moving charge experiencing a force
• Apply the right-hand rule to determine the direction of a magnetic force based on the motion of a charge in a magnetic field
• Sketch magnetic field lines to understand which way the magnetic field points and how strong it is in a region of space

#### 7.3 Motion of a Charged Particle in a Magnetic Field

• Explain how a charged particle in an external magnetic field undergoes circular motion
• Describe how to determine the radius of the circular motion of a charged particle in a magnetic field

#### 7.4 Magnetic Force on a Current-Carrying Conductor

• Determine the direction in which a current-carrying wire experiences a force in an external magnetic field
• Calculate the force on a current-carrying wire in an external magnetic field

#### 7.5 Force and Torque on a Current Loop

• Evaluate the net force on a current loop in an external magnetic field
• Evaluate the net torque on a current loop in an external magnetic field
• Define the magnetic dipole moment of a current loop

#### 7.6 The Hall Effect

• Explain a scenario where the magnetic and electric fields are crossed and their forces balance each other as a charged particle moves through a velocity selector
• Compare how charge carriers move in a conductive material and explain how this relates to the Hall effect

#### 7.7 Applications of Magnetic Forces and Fields

• Explain how a mass spectrometer works to separate charges
• Explain how a cyclotron works