• ### Unit 4: Magnetism

Now that we have studied electric charges, potentials, and fields, let's look at the effect of moving charges: magnetism. Thales of Miletus set the stage for the scientific exploration of magnetism back in Ancient Greece, when he could only observe magnetism via the behavior of natural magnets, called lodestones.

Hans Christian Oersted documented the relationship between moving electric charges and magnetism much later, in 1820 when he accidentally discovered that an electric current could deflect a nearby compass needle. James Clerk Maxwell united electrical and magnetic phenomena into four reasonably simple equations, which we know as Maxwell's Equations, 45 years after Oersted made his observation.

The discovery that electrical currents cause magnetic effects led to the invention of the galvanometer, which we have already encountered as the core component of ammeters and voltmeters.

Completing this unit should take you approximately 7 hours.

• ### 4.1: Magnets

A magnet is a material or object that creates a magnetic field. While the magnetic field is invisible, it creates a force that pulls on other ferromagnetic materials, such as iron, steel, nickel, and cobalt. It can also attract or repel other magnets. While a magnet attracts these examples of magnetic materials, non-magnetic materials, such as rubber, coins, feather and leather, are not attracted.

• ### 4.2: Magnetic Field

In these readings, we encounter a tool you will recognize from our discussion of electric fields: field lines. But their meaning is quite different in this context. In the case of electric field lines, the direction of the line shows you in what direction a positive test charge will be pulled. However, a magnetic field line shows you the direction in which a little compass needle will align itself!

• ### 4.3: Magnetic Force on Moving Electric Charges

In the video we just watched, it is essential to realize how different magnetism is from electrostatic forces. For example, when you place a magnet near a negatively-charged balloon, there will be no force whatsoever between the two. But when a single negatively-charged electron flies past the same magnet, it will feel a force (even though its charge is much smaller than the charge on the balloon). It is the speed of the electron that makes all the difference. Only moving charges are affected by magnetic fields.

We call the force felt by the moving, charged object the Lorentz force. The logic behind this force is a little different from what we did in electrostatics, because at this point we do not know how to calculate the strength and direction of a magnetic field using a formula analogous to Coulomb's Law (the formula that relates the electric force to charges).

What we are doing instead is a sort of reverse logic. Let's assume a magnetic field has somehow been created. Now try to characterize the strength and direction of that field quantitatively. As with electricity, you can think of the magnetic field as a would-be magnetic force. So, to characterize the field, we need to measure a force. This could be the force that twists a compass needle away from the Earth's north-south direction, or it could be the force that deflects a moving charge.

• ### 4.4: Magnetic Force on a Current-Carrying Wire

Electric currents typically consist of huge numbers of electric charges that move in a coordinated, overall motion. However, unless you see it heat up and start glowing, it is not easy to tell from the outside whether a wire is carrying a current or not. One difficulty is that even the strongest currents will not create any electrostatic force anywhere along the length of wire, at macroscopic distances.

This is because a conductor remains electrically neutral while electrons move through it. Any excess electrons that enter a segment of the wire on one end will simultaneously be made up for by electrons leaving that segment on the other end. Remember, the conductor contains equally many positive charges in the nuclei of its atoms, as there are electrons in it.

This is why magnetism is the best way to detect and quantify how many amperes of current is going through a circuit. It is created by the motion of the negatively-charged electrons that make up the current, whereas the positively-charged nuclei have no magnetic effect because they are not moving! So while the electric influences of electrons and nuclei cancel out as seen from the outside, their magnetic effects do not.

• ### 4.5: Magnetic Fields Produced by Currents: Ampère's Law

Until now we have primarily discussed magnetism in situations where the magnetic field is already there, and we place some type of moving object under its influence. Now, we finally return to our question: how are magnetic fields created in the first place, and what determines their strength?

As Oersted observed, currents create magnetic fields. But we would like to have a formula that says how the strength of the field is related to the amount of current.

An electromagnet uses an electric current to create the same magnetic forces we have just discussed. We use electromagnets for everything from a crane in a wrecking yard which lifts scrapped cars, to controlling the beam of a 90-km-circumference particle accelerator, to the magnets in medical imaging machines. But if you look at an electromagnet closely, it is nothing but a loop (or coil) of wire, just like the coils we just saw in motors and meters!

How can we use the same device (a coil) for two different purposes: creating a force on a current, as in a motor, and turning a current into a magnetic field?

If you think about it, the answer is actually not that surprising if you keep Newton's Third Law in mind: action equals reaction. In a motor, a magnet created a force on the current-carrying coil via the magnetic field. By Newton's Third Law, the current-carrying coil must simultaneously be exerting a force on the magnet. That is the magnetic field created by the coil, and it makes the coil an electromagnet.

• ### 4.6: Magnetic Force Between Two Parallel Conductors

Originally, the name Ampère's Law described a discovery André-Marie Ampère made soon after Oersted's first report of magnetism from current-carrying wires. You can view it as an example of Newton's Third Law in action, because it puts the "source" and "recipient" of a magnetic force on equal footing, as they should be if action and reaction are equal.