Magnetic Flux

Whenever you are studying magnetism, among the key fundamental variables you must analyze is the magnetic flux.

It will help you understand the effects of magnetic fields on objects. Besides, it forms the basis for describing certain laws in magnetism such as Lenz and Faraday’s Law of Induction.

What is Magnetic Flux?

First, let’s start by defining a magnetic field.

A magnetic field is a region or an area around magnets where you can detect magnetic force. It is within this region that the magnetic force is distributed around a magnet.

Therefore, magnetic field lines are “imaginary paths” illustrating the effect of magnetic strength. They collectively form a magnetic field.

Usually, they move from the magnet’s north pole to south-pole. Moreover, the magnetic field lines are more concentrated around the magnet poles. However, they tend to spread outwards as they move away from the magnet pole.

Now, a magnetic flux is the total magnetic strength passing through a given area. That is to say, it is the total number of field lines that pass within a specific surface area. It is from this fact that we have the magnetic flux formula:

We will explore more about the formula and equation shortly.

Symbol and Formula for Magnetic Flux

For the Magnetic Flux, we denote it using the Greek letter Phi. The symbol for Magnetic Flux is Φ.

In most calculations, you will encounter this symbol. This is quite clear as you can see in the magnetic flux formula below:

For a normal flat surface, we have the formula:

In situations where the surface makes an angle, then the formula will be:

From the above the letters and symbols represent:

  • A for surface area
  • B which demotes the magnetic field
  • θ is the angle between the surface and the normal line.
  • Φ refers to the magnetic flux

Calculating Total Magnetic Flux

With the advancement in technology, you can use online software to calculate the total magnetic flux. Still, even with these online calculators, you need certain variables such as;

  • Angle of incidence
  • Magnetic field strength
  • Cross-section area

Alternatively, once you have these figures, use a calculator to get the exact values.

Magnetic Flux Density

When you place a wire at 90 degrees to the magnetic field, there will be a net force that will act on the wire for every current that passes through within a given unit length. It is this force on the wire that we refer to as magnetic flux density.

It is important to note that magnetic flux density is a vector quantity. Therefore, we denote it with the letter B. To calculate magnetic flux density, we use the formula:

In the equation above you have the:

  • F is the force that acts on the wire due to the magnetic field
  • I is the current that passes through the wire
  • L represents the length of wire in the magnetic field.

It is also worth mentioning that we measure the magnetic flux density in Tesla (T) or Kg s¯² A¯1

Role of Magnetic Flux in Laws of Magnetism

Many laws of magnetism or magnetic induction depend on magnetic flux or magnetic flux density.

Let’s look at some common laws are their relation to the magenta flux.

Faraday Law of Induction

It is Michael Faraday who discovered interesting attributes of a changing magnetic flux. Through various experiments, Faradays concluded that:

Whenever there is a change in magnetic flux, an electric current will ultimately be induced in a coil. Usually, we refer to this as an induced voltage or electromagnetic force.

The law states that “changes in magnetic flux over time can induce an electric current in the coil having an electromagnetic force (EMF) or induced voltage.”

We can express this law using the equation:

Where: ΔΦ shows the magnetic flux changes

: Δt change in time

Again the negative sign shows Lenz’s law. This law states that induction opposes any change in magnetic flux.

Gauss Law of Magnetism

Guess law states that in any closed surface, the net magnetic flux will always be zero. That is to say, magnetic fields that enter a surface will be equal to those exiting.

You can use Gauss law to detect magnetic fields due to symmetry among other applications.

How to Measure Magnetic Flux

First, the values you obtain for magnetic flux are always in:

  • Weber (Wb) or,
  • Tesla meter squared (Tm²)

In today’s industries, a flux meter is a common instrument for determining magnetic field flux. Alternatively, you can use a magnetometer.

Remember, the SI unit is named after the famous German physicist Wilhelm Weber who co-invented the telegraph. Let us take an example of a magnetometer placed inside an area measuring 1m².

This area is next to a large magnetic material that gives a reading of 10mT. We can calculate the Magnetic flux to get:

Note: For the above calculations, we use the formula we mentioned earlier.

Importance of Vector Field in Magnetic Field

When examining magnetic flux, you must evaluate the vector field. The knowledge on vector field will give you insights on:

  • The behavior of physical quantity
  • Properties of the physical quantity

Through these, you will learn more about other aspects such as force, and velocity, among other important variables.

On the other hand, through magnetic flux, you will get more insights into the behavior of magnetic fields within a specific area or surface.

In a nutshell, magnetic flux depends on:

  • Magnitude of magnetic field
  • Direction of magnetic field
Applications of Magnetic Flux

There are many areas where the knowledge of magnetic flux plays an integral role. Some of the most common applications include:

· Electrical Industry

It plays an important role when determining the amount of power an electric generator produces. Additionally, we use it in transformers to control the amount of current and voltage that flows in it.

· Automotive Industry

Alternators and electric motors in cars rely a lot on the magnetic flux for their operations. We also use the Magnetic Flux in sensors to detect position, speed, and other parameters.

· Aerospace Industry

Some very critical instruments such as altimeters and compasses in aircraft use magnetic flux in their functions. The aircraft is also shielded from any form of radiation using the electromagnetic fields generated from magnetic flux.

· Medical Industry

During scans, internal body structure images can be produced using the MRI machine relying on magnetic flux. The human brain activities can also be stirred therapeutically using Magnetic Flux principles.

· Defense Industry

The military makes use of magnetic detectors to receive any form of magnetic interference in sensitive areas. They also use magnetic flux principles to locate any submarine signals coming from under the waters.

Is Magnetic Field Strength the same as Magnetic Flux?


First, we use the Greek letter Phi and the symbol Φ to refer to magnetic flux density. On the other hand, we use H to represent magnetic field strength.

Usually, H refers to the measure or magnitude of the magnetic field within a specific region. So remember, with the magnetic flux, it consider the field passing through a given area.

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