What Causes Different Strengths In Magnets?

Many people are familiar with magnets because they often have decorative magnets on their kitchen fridge. However, magnets have many practical purposes beyond decoration, and many affect our daily lives without us even knowing it.

There are a lot of questions about how magnets works, and other general magnetism questions. However, to answer most of these questions, and to understand how different magnets can have different strengths of magnetic fields, it is important to understand what a magnetic field is and how it is produced.

A magnetic field is a force that acts on a charged particle, and the governing equation for this interaction is the ​Lorentz force law.​ The full equation for the force of an ​electric field​ ​E​ and a ​magnetic field B​ on a particle with charge ​q​ and velocity ​v​ is given by:

\(\vec{F} = q\vec{E} + q\vec{v}\times \vec{B}.\)

Remember that because the force ​F​, the fields ​E​ and ​B​, and the velocity ​v​ are all vectors, the ​×​ operation is the ​vector cross product​, not multiplication.

Magnetic fields are produced by moving charged particles, often called ​electrical current​. Common sources of magnetic fields from electrical current are electromagnets, such as a simple wire, a wire in a loop, and several loops of wire in a series which is called a ​solenoid​. The earth's magnetic field is also caused by moving charged particles in the core.

However, those magnets on your fridge do not seem to have any flowing currents or power sources. How do those work?

A permanent magnet is a piece of ​ferromagnetic material​ that has an intrinsic property that produces a magnetic field. The intrinsic effect that produces a magnetic field is an electron spin, and the alignment of these spins creates magnetic domains. These domains result in a net magnetic field.

Ferromagnetic materials tend to have a high degree of domain ordering in their naturally occurring form, which can easily be entirely aligned by an external magnetic field. Thus ferromagnetic magnets tend to be magnetic when found in nature and easily retain their magnetic properties.

​Diamagnetic materials​ are similar to ferromagnetic materials and may produce a magnetic field when found in nature, but respond to external fields differently. Diamagnetic material will produce an oppositely oriented magnetic field in the presence of an external field. This effect could limit the desired strength of the magnet.

​Paramagnetic materials​ are only magnetic in the presence of an external, aligning magnetic field, and tend to be fairly weak.

As mentioned, permanent magnets consist of magnetic domains that align randomly. Within each domain, there is some degree of ordering which creates a magnetic field. The interaction of all of the domains in one piece of ferromagnetic material therefore produces the overall, or net, magnetic field for the magnet.

If the domains are randomly aligned, it is likely that there may be a very small, or effectively zero magnetic field. However, if an external magnetic field is brought close to the unordered magnet, the domains will begin to align. The distance of the aligning field to the domains will affect the overall alignment, and therefore the resulting net magnetic field.

Leaving a ferromagnetic material in an external magnetic field for a long period of time can help with completing the ordering, and increasing the produced magnetic field. Similarly, the net magnetic field of a permanent magnet can be decreased by bringing in several random or interfering magnetic fields, which can misalign the domains and reduce the net magnetic field.

Does the size of a magnet affect its strength? The short answer is yes, but only because the size of a magnet means that there are proportionally more domains that can align and produce a stronger magnetic field than a smaller piece of the same material. However, if the length of the magnet is very long, there is an increased chance that stray magnetic fields will misalign domains and decrease the net magnetic field.

Another contributing factor the magnet strength is ​temperature​. In 1895, French physicist Pierre Curie determined that magnetic materials have a temperature cutoff at which point their magnetic properties can change. Specifically, the domains no longer align as well, thus the week domain alignment leads to a weak net magnetic field.

For iron, the Curie temperature is around 1418 degrees Fahrenheit. For magnetite, it is around 1060 degrees Fahrenheit. Note that these temperatures are significantly lower than their melting points. Thus, the temperature of the magnet can affect its strength.

A different category of magnets are ​electromagnets​, which are essentially magnets that can be turned on and off.

The most common electromagnet that is used in various industrial applications is a solenoid. A solenoid is a series of current loops, which result in a uniform field in the center of the loops. This is due to the fact that each individual current loops creates a circular magnetic field about the wire. By placing several in series, the superposition of the magnetic fields creates a straight, uniform field through the center of the loops.

The equation for the magnitude of a solenoidal magnetic field is simply: ​**B = μ₀nI**​, where ​_μ₀ ​is the permeability of free space, ​n​ is the number of current loops per unit length and ​I_​ is the current that is flowing through them. The direction of the magnetic field is determined by the right-hand rule and the direction of the current flow, and therefore can be reversed by reversing the direction of the current.

It is very easy to see that the strength of a solenoid can be adjusted in two primary ways. First, the current through the solenoid can be increased. While it seems like the current can be arbitrarily increased, there may be limitations on the power supply or the resistance of the circuit, which may result in damage if the current is overdrawn.

Therefore, a safer way to increase the magnetic strength of a solenoid is to increase the number of current loops. The magnetic field clearly increases proportionally. The only limitation in this case may be the amount of wire that is available, or spatial limitations if the solenoid is too long due to the number of current loops.

There are many kinds of electromagnets besides solenoids, but all have the same general property: Their strength is proportional to the current flow.

Electromagnets are ubiquitous and have many uses. A common and very simple example of an electromagnet, specifically a solenoid, is a speaker. The varying current through the speaker causes the strength of the solenoidal magnetic field to increase and decrease.

As this happens, another magnet, specifically a permanent magnet, is placed at one end of the solenoid and against a vibrating surface. As the two magnetic fields attract and repel due to the changing solenoidal field, the vibrating surface is pulled and pushed creating sound.

Better quality speakers use high-quality solenoids, permanent magnets, and vibrating surfaces to create higher quality sound output.

The largest size magnet in the world is the earth itself! As mentioned, the earth has a magnetic field which is due to the currents created with the core of the earth. While it is not a very strong magnetic field relative to many small handheld magnets or the once used in particle accelerators, the earth itself one of the largest magnets we know of!

Another interesting magnetic material is magnetite. Magnetite is an iron ore that is not only very common but is the mineral with the highest iron content. It is sometimes called lodestone, due to its unique property of having a magnetic field that is always aligned with the earth's magnetic field. As such, it was used as a magnetic compass as early as 300 BC.