xaktly | Physics | E & M


The second invisible force

We are all familiar with gravity, the invisible force that holds us to Earth and that accounts for all of the motion of stars planets and other bodies in the universe.

You are probably familiar with magnetism, an invisible force between two objects. You've noticed several characteristics of magnets, including:

  • Magnets have two ends, called poles.
  • Like poles repel each other (Note that gravity is solely an attractive force!).
  • Opposite poles attract.
  • The magnetic force depends on the distance between magnets. It's strong close up and weak far away.
  • Magnets stick to certain kinds of materials which are not magnets, like steel, but not aluminum.

In this section we'll discuss permanent magnets. We'll look at what makes things magnetic, kinds of magnetic properties and the shapes of magnetic force fields.

In another section we'll discuss how magnetic fields can be generated by electric current flowing through a wire.

It turns out that electricity and magnetism are intertwined, and in many situations, we can't talk about one without addressing the other. In fact, we very often refer not to electrical or magnetic phenomena, but to electromagnetic phenomena.

Origin of magnetism

The phenomenon of magnetism has been known of since about 600 BC, when both Greeks and Indians observed that certain stones – lodestones – attracted iron metal (the beginning of the iron age was between 1200 BC and 600 BC, depending on the region). After gravity, it was the second invisible force to be discovered.

Lodestone is a word for one of a few minerals of iron, the most common one being magnetite, Fe3O4, or more properly, Fe2+Fe23+O42-, indicating that it contains both Fe(II) and Fe(III) ions. Magnetite is a crystal with a well ordered structure, depicted here from experimental data. The red spheres are oxygen atoms and the green and black spheres are Fe3+ and Fe2+, respectively.

Source: Wei Wu et al. "Recent progress on magnetic iron oxide nanoparticles: Synthesis, surface functional strategies and biomedical applications," Science & Tech. of Adv. Mat., April (2015).

The order of magnetite crystals leads partially to their magnetism, but that's not the root of it.


Magnetism in a material is generated by the "spins" of electrons in the atoms that compose it. The word "spin" is in quotes because it isn't really the case that electrons are spinning. (See electrons for more on electron spin.) They simply possess a property that, when it was first discovered, showed similar properties to spinning charged objects. The spin property of electrons turns them into small magnets, each with a north and south pole.

You can read more about the unique properties of electrons here.

Normally, compounds do not exhibit magnetism because:

  • the spins of electrons are paired in electronic orbitals and therefore cancel, or

  • unpaired spins aren't well-aligned with one-another, and point in more-or-less random directions, leading to no clear direction for north and south poles of the material.

Because of the nice ordering of iron ions in magnetite crystals, the spins of iron atoms can align and reinforce a permanent magnetic moment in the material.

The protons and neutrons inside of nuclei also have the property of spin, but their contribution to magnetism is much smaller than that of electrons. Proton spins are important when we subject them to large external magnetic fields, such as in a medical MRI (magnetic resonance imaging) machine, or in an NMR (nuclear magnetic resonance) spectrometer in the laboratory.

Magnets always have two poles (or do they?)

Any magnet you can find will have a north and south pole. This figure illustrates that even if we cut a magnet in half, the two halves will exhibit the same polar properties: The new magnets will instantly develop new poles to become dipolar. A bar magnet is an example of a magnetic dipole.

It doesn't matter how small the magnet is, we still observe that all magnets have two poles. Contrast this to charges. While a positive and a negative charge form a dipole (which has an electric field similar to the magnetic field of a bar magnet), it is also possible for positive and negative charges to be isolated. In fact we can create streams or "beams" of negatively- or positively-charged particles.

Magnetic monopoles?

There doesn't seem to be any theoretical barrier to finding a magnetic monopole – an isolated north or south pole, but to date, none have been observed.

The equations that describe classical electromagnetic phenomena, Maxwell's equations, allow for magnetic monopoles. Maybe you can be the one to discover them.

Classification of materials by magnetic properties

There exist a relatively small variety of materials, usually crystalline (which means dependable order in the structure), that are naturally magnetic. That is, when formed, unpaired electrons exist in each repeating component (unit cell) of the crystal, and the resulting unpaired spins align, each a small magnet, to form a larger permanent magnet.

There are only a few kinds of permanent magnets, from magnetite to the very strong neodymium magnets (actually Nd2F14B) now used in modern motors and other devices. These materials are called ferromagnetic. The word (ferro / ferrum = iron) originates from early observations that only iron compounds were permanently magnetic.

Here is a simple representation of a permanent magnet. The spheres stand for unpaired electron spins, each with a north and south pole – each a tiny magnet.

The arrow points toward the north pole of the magnet, the general direction of all tiny poles. In reality, the spins are never so exactly aligned, and every atom, even at very low temperatures, is always in motion. But the average orientation of the spins has a strong alignment that produces permanent magnetism.

Paramagnetic materials

In contrast, non-magnetic materials that have unpaired spins might look something like this figure. The spins are not aligned, thus there is no overall direction to the magnetic force exerted by the their sum. These materials can be paramagnetic.

We know that placing a magnet near a compass can cause the needle to swing around. The schematic above suggests that if we place such a material near a permanent magnet, the permanent magnet might induce some alignment of spins within the substance, called a paramagnetic material, that could magnetize it. The animation below shows schematically how that occurs. Play it a few times to get the idea: When a paramagnetic material is placed in the field of a permanent magnet, its unpaired spins can align, making it magnetic. It's why permanent magnets will stick to metals, like steel, that contain iron atoms. Ferromagnets can essentially cause paramagnetic materials to become extensions of their own magnetism.


The term diamagnetic describes materials that don't show any tendency to become magnetized. The electron spins of their constituent atoms are fully paired, and thus don't create a magnetic moment.

All materials possess some atoms with paired spins, even ferromagnetic materials, so there is always some degree of nonmagnetic character in any magnet. It's one of the things inventors of new magnets try to minimize.

Purely diamagnetic materials weakly repel magnets, but the force is much weaker than the magnetic force.

Summary of magnetic classifications

Classification Examples Characteristics
ferromagnetic magnetite, hematite Unpaired spins are aligned in a crystalline material.
paramagnetic magnesium, iron, lithium, molybdenum & others Unpaired spins are present, but unaligned. They can be aligned in the presence of a strong magnetic field.
diamagnetic most materials No unpaired spins to interact with an external magnetic field.

Permanent magnets & magnetic fields

Permanent magnets, being made mostly of metallic elements, can be formed into a variety of useful shapes, each of which produced a different field of forces on other magnetic materials. We call that field the magnetic field, or sometimes B-field.

Magnetic fields are analogous to the electric fields produced by charged particles.

The simplest permanent magnet is a bar magnet, just a rod of ferromagnetic material. All magnets have two poles, which we call north and south for how they relate to the large magnet upon which we live, planet Earth. Earth has a ferromagnetic core of molten iron, which produces a magnetic field that we can detect, and indeed use for navigation.

The magnetic field of a bar magnet looks like this:

The blue lines are the direction of the force on a compass needle, were it placed at a particular location near the bar magnet.

Roll over / tap the diagram to see how small compasses, placed at various points in the field, would point. Notice that they point along the field lines, with the north (red) arrow of the compass pointing toward the south pole of the magnet.

Like an electric field, in places where the field lines are the most dense, the magnetic force is the strongest. Notice that our test magnets align so that the north (red) end of the compass points along a the field toward the south end of the bar magnet.

Magnets can come in many shapes. Here is a schematic picture of the field lines of a common horseshoe magnet.

Magnetic field strength

The strength of a magnetic field is measured in two main units. The SI unit of field strength is the Tesla ( T ).

Another common unit (still in use because it keeps the numbers on a manageable scale) is the Gauss (G).

1 G = 1 × 10-4 T

Magnetic field strength is tricky to measure, so we'll forgo discussing measurements and calculations here.

A strong MRI (magnetic resonance imaging) scanner in a hospital or clinic can have a field strength of 3 T, while the magnetic field of Earth is, on average, about 50 μT at the surface.


SI units

SI stands for Système international (of units). In 1960, the SI system of units was published as a guide to the preferred units to use for a variety of quantities. Here are some common SI units


Earth's magnetic field

Our planet is a giant magnet. Current theory suggests that electric currents circulating in its molten core form an electromagnet. This is consistent with evidence suggesting that the north-south direction of the field has reversed a few times in Earth's history. The average strength of the field is about 50 microTeslas (μT), or about 0.5 Gauss, enough to cause a lightweight magnet like a compass needle to align with the field lines, which are roughly illustrated below.

The magnetic field of Earth is tilted about 11˚ away from the rotational axis of the planet (in the rough direction of Greenland). The rotational axis passes through what we know as the north and south poles on a map (true north and true south). Indeed, maps are usually drawn so that the vertical lines (meridians) are parallel to that axis.

The difference between the rotational and magnetic poles has a consequence for us when we're using a compass for navigation. In order to align a map properly along the north-south line, we need to account for the fact that our compass will not be pointing exactly to true north, but to magnetic north.

The blue map of the United States shows isogonic lines, along which the angle between magnetic and true north is constant. East of a line passing through Illinois and Alabama (the agonic line), the compass will point to the west of true north, producing what we call a west declination. True north lies 20˚ to the east of where the compass is pointing. To the west of the agonic line we find east declinations up to 20˚ in the 48 contiguous US states, meaning that true north lies a number of degrees to the west of what the compass says.

For example, if you wanted to use your compass properly on Mt. Washington in New Hampshire, you'd have to adjust for a 17˚ west declination. True north would be 17˚ to the east of what your compass needle says.

Magnetic declination is the angle from true north to magnetic north as observed from some point on Earth.

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