Magnetic fields

Tiny rod-shaped iron particles aligning with the magnetic field of a bar magnet

Recalling electric fields

In my post on electric fields, I described how electric fields are like lines of force that emanate from positive charges and converge on negative charges, as shown in this picture.

Electric field produced by a positive charge and an equal negative charge

These lines show us a map of the force that would act on a third charge if it were to be introduced into the picture. If this third charge were positive, the electric field lines show us straightforwardly its repulsion from the first positive charge and its attraction to the negative charge. The more closely spaced the lines, the stronger the force.

How are magnetic fields produced differently?

Magnetic fields can also be pictured in this way. We know that a bar magnet has two poles, north (N) and south (S). When we play with two bar magnets, we find that like poles repel and opposite poles attract. So we might be tempted to think that the N pole is a positive "magnetic charge" out of which magnetic field lines emanate and that the S pole is a negative "magnetic charge" into which magnetic field lines converge. If you look for images on stock photo sites, you can find pictures like this:

Incorrect picture of the magnetic field of a bar magnet

This picture is incorrect! One of Maxwell's equations states that there is no such thing as a magnetic charge where magnetic field lines converge or diverge. Magnetic field lines always form closed loops. Here's a correct picture of the magnetic field of a bar magnet. Each line goes through the magnet from S to N, takes a path around the outside, and then comes back into the S pole to complete a full loop. (Most of the loops shown are too big to fully fit in the picture.)

Left: Magnetic field of a bar magnet, N pole on the right, S pole on the left. Geek3, CC BY-SA 4.0 <https://creativecommons.org/licenses/by-sa/4.0>, via Wikimedia Commons Right: Maxwell and his equation saying that the magnetic field (or B field) must form closed loops

So if there are no magnetic charges, what produces magnetic fields? Michael Faraday and others discovered that magnetic fields are created by electrical currents, in other words, by charges in motion. For example, electrical current flowing through a wire (which is caused by moving electrons) creates magnetic field lines that loop around the wire, as shown below. Another one of Maxwell's equations, part of which is shown below on the right, expresses the relationship between the magnetic field and the current producing it. (In a bar magnet, electrons either spinning or orbiting around atoms create microscopic loops of current flow, and this produces the bar magnet's field.)

Left: Electrical current flowing up through a wire creates magnetic field lines that circle around the wire. Right: Maxwell' equation expressing the relationship between magnetic field (B) and current (J).

How do magnetic fields produce forces differently?

Just as magnetic fields are produced by moving charges, they also create forces on moving charges. But these forces are a bit weird, because they always push the charge sideways. The force is at right angles both to the direction the charge moves and to the magnetic field. For example, if a positive charge moves east through a magnetic field (produced by something else) that points north, then the charge will be pushed upward! Faraday demonstrated a primitive motor based on this. Here is a sketch of the demonstration.

Faraday's motor demonstration

A magnet is placed in a bowl of liquid. The liquid is a good conductor of electricity, such as salt water. A battery is wired to the system to create an upward current flow through a wire that is suspended into the liquid and free to rotate at the top (orange wire in the above picture). As the charge flows upward through this wire, it goes through the magnetic field produced by the bar magnet, which points outward away from the center. This creates a force that is at right angles to both the current and the magnetic field. In the above figure, this force is into the page, causing the wire to stir the liquid in a counterclockwise direction as viewed from above. Here's an article with a video of this motor. This first motor wasn't powerful enough to do anything useful, but it demonstrated the physics.

The Earth is a magnet

Circulation of the molten iron in the Earth's core creates loops of electrical current flow. So the Earth is a giant bar magnet. We can see from this picture that the geographic poles of the Earth are, in a sense, misnamed. The north magnetic pole, magnetically speaking, corresponds to the south pole of a bar magnet.

Earth's magnetic field. The field inside the Earth is not shown, but the field makes closed loops.

A traditional compass is a small bar magnet. The forces I've described cause it to align, as much as it can, with the Earth's magnetic field. This works well near the equator and at mid latitudes where the Earth's magnetic field points mostly north. As one gets closer to either the North or South Pole, the Earth's magnetic field lines become more and more vertical and then a compass doesn't work well.

A compass

Magnetic fields are useful!

Magnetic fields are used, as already pointed out, for navigation and to make motors. Electric generators use magnets. Trains can be levitated using magnetic fields, minimizing friction. Magnetic fields are used to investigate the properties of matter, because atoms can be manipulated by magnetic fields and we can measure how they respond. In medicine, a powerful tissue imaging technique, magnetic resonance imaging (MRI), is based on measuring the response of tissue to magnetic excitations.

The discussion in this post and the electric fields post are about steady electric and magnetic fields. Other parts of Maxwell's equations, which I haven't shown, state that electric and magnetic fields are intertwined. A changing electric field creates a magnetic field and vice versa. This leads us into light waves and radio waves, a topic for another post.