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What Is Magnetic Flux?

By Jason C. Chavis
Updated May 21, 2024
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Magnetic flux is the quantity of magnetic field that penetrates an area at right angles to it. In a simple situation where the field passes at right angles through a flat surface, this quantity is the strength of the magnetic field multiplied by the area of the surface. In most real-life situations, however, other factors have to be taken into account. Magnetic flux is an important concept in many areas of science, with applications relating to electric motors, generators and the study of the Earth’s magnetic field. It is represented in physics by the Greek letter phi, φ.

Gauss’s Law

A bar magnet has two poles, named north and south due to the way they react to the Earth’s magnetic field, which is aligned roughly north-south. It is a scientific convention that the lines of magnetic force flow from north to south. If a person takes the two dimensional rectangular surface at the north end of a bar magnet, it has a magnetic flux, as does the surface at the south pole. The magnet as a whole, however, has no flux, as the north and south ends are equal in strength and the field “flows” from the north pole into the south pole, forming a closed loop.

Gauss’s law for magnetism states that, for a closed surface, such as a sphere, a cube or a bar magnet, the magnetic flux is always zero. It is another way of saying that an object, no matter how small, with a north pole must always have a south pole of equal strength and vice versa. Everything that has a magnetic field is a dipole, meaning that it has two poles. Some scientists have speculated that magnetic monopoles may exist, but none have ever been detected. If they are found, Gauss’s law would have to be changed.

Faraday’s Law

Faraday’s Law states that a change in magnetic flux will create a voltage, or electromotive force (EMF), within a coil of wire. Simply moving a magnet near a coil of wire will achieve this, as will a change in the strength of the magnetic field. The voltage produced can be determined from the rate of change in magnetic flux and the number of turns in the coil.

This is the principle behind electricity generators, where movement is created by, for example, running water, wind, or an engine powered by fossil fuels. Magnets and coils of wire convert this movement into electrical power, in accordance with Faraday’s Law. Electric motors demonstrate the same idea in reverse: an alternating electric current in coils of wire interacts with magnets to produce movement.

Magnetic Materials

Materials vary in their reactions to magnetic fields. Ferromagnetic substances produce a stronger magnetic field of their own, and this field may persist when the external field is removed, leaving a permanent magnet. Iron is the best-known element of this type, but other metallic elements, such as cobalt, nickel, gadolinium, and dysprosium, also demonstrate this effect. Very powerful magnets can be made from alloys of the rare earth metals neodymium and samarium.

Paramagnetic materials produce a magnetic field in response to an external one, producing a relatively weak attraction that is not persistent. Copper and aluminum are examples. Another example is oxygen; in this case, the effect is best demonstrated with the element in liquid form.

Diamagnetic substances create a magnetic field that is opposed to an external field, producing repulsion. All substances show this effect, but it is normally very weak and always weaker than ferromagnetism or paramagnetism. In a few cases, such as a form of carbon called pyrolytic graphite, the effect is strong enough to allow a small piece of material of this type to float in the air just above an arrangement of strong magnets.

Calculating and Measuring Flux

Calculating the flux for a flat surface at right angles to the direction of a magnetic field is straightforward. Often, however, it is necessary to calculate the quantity for a coil of wire, also known as a solenoid. Assuming the field is perpendicular to the wire, the total flux is the magnetic field strength multiplied by the area through which it passes multiplied by the number of turns in the coil. Where the field is not at right angles to the surface, the angle made by the magnetic field lines to the perpendicular must be taken into account, and the product is multiplied by the cosine of this angle.

An instrument called a fluxmeter is used to measure the quantity of the field. It relies on the fact that a magnetic field will create an electrical current in a wire if the two are moving relative to one another. This current can be measured to determine the flux.

Magnetic Flux in Geology

The measurement of magnetic flux at various points on the Earth’s surface enables scientists to monitor the planet’s magnetic field. This field, thought to be generated by electric currents in the Earth’s iron core, is not static, but shifts over time. The magnetic poles have, in fact, reversed many times in the past and will likely do so again in the future. The effects of a pole reversal may be serious, as during the change, the strength of the field would be reduced over much of the planet. The Earth’s magnetic field protects life on the planet from the solar wind, a stream of electrically charged particles from the Sun that would be harmful.

Units of Measurement

The strength of a magnetic field, or the magnetic flux density, is measured in Teslas, a unit named after the electrical engineer Nikola Tesla. The flux is measured in Webers, named after the physicist Wilhelm Eduard Weber. A Weber is 1 Tesla multiplied by 1 square meter, and a Tesla is 1 Weber per square meter.

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Discussion Comments

By KoiwiGal — On Aug 29, 2012

A true definition of magnetic flux is considered a fairly advanced concept in physics and is often broken down into a simpler explanations. I've never been able to really grasp the more advanced (and actually shorter) definition of magnetic flux but this article does a good job at defining it in a simple way.

What really amazes me is that someone must have worked out all these laws and definitions once without someone around to write handy articles. One of the components of magnetic flux is named after Nikola Tesla, so I wonder if he helped to figure out this scrap of science with his experiments in magnetism.

By irontoenail — On Aug 28, 2012

I read a short story the other day what speculated on what would happen if the magnetic poles of Earth switched around. That sounds like something the author just made up, but really it's a possibility. It happens every so often (as in, every million years or so) and we are getting close to the point where it becomes more likely that it will happen.

It's not going to be the end of the world, but there could be all kinds of consequences, for example on our atmosphere, and our electronic communication, while the poles change.

It's amazing how much is based around the magnetic flux of the planet and depends on it staying stable in order to work.

By anon89436 — On Jun 10, 2010

you really know how to express this subject but have failed to get the meaning of magnetic flux density. Thank you very much for enabling us (students) to have a chance to know about physics.

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