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# Magnetic Flux – Symbol, Unit, Conclusion and FAQs

Aug 13, 2022

## Magnetic Flux

Magnetic flux is a concept in electromagnetism, a part of Physics. Magnetic flux across a given surface can be defined as the magnetic field’s normal component’s surface integral that passes through that particular surface. It can be represented by ΦB or Φ. Maxwell is the CGS unit of magnetic flux, while Weber (Wb) is its SI unit.

### What is Magnetic flux?

It is the magnetic field lines passing across a given closed surface. It helps us quantify the total magnetic field passing through a particular surface area. The area under consideration here can be of any size and orientation with respect to the magnetic field’s direction.

### Symbol of Magnetic Flux

• The Greek letter Phi suffix B or Phi is generally used to denote the magnetic flux.
• The symbol of magnetic flux is ΦB or Φ.
• The formula of magnetic flux is given by:

Here,

ΦB stands for the magnetic flux.

A represents the area where the flux is acting.

B represents the magnetic field

θ is the angle at which the magnetic field lines cross the given surface area

### Unit of Magnetic Flux

We can measure the magnetic flux with the help of a flux meter. The CGS and SI units of magnetic flux are:

• The CGS unit of magnetic flux is Maxwell
• Weber (Wb) is the SI unit of magnetic flux
• The fundamental unit of magnetic flux is Volts-seconds.

### The Formula of Magnetic Flux:

The magnetic flux formula is:

Φ=→B∗→A=B∗A∗cos(θ)Φ=B→∗A→=B∗A∗cos(θ)

Where,

• Magnetic flux is denoted by B, ΦB
• B is the magnetic field.
• The region is A.
• ‘θ‘  The angle at which the field lines cut across the specified surface area

#### Magnetic Flux Measurement

In honor of German physicist Wilhelm Weber, the SI unit of magnetic flux is the Weber (Wb) or tesla meter squared (Tm2) A magnetometer can calculate the magnetic flux. Consider moving a magnetometer probe over a 0.6 m2 region near a sizable sheet of magnetic material while it continuously registers a reading of 5 mT. Following that, the magnetic flux through that region is computed as (5 10-3 T) (0.6 m2) = 0.0030 Wb. It would be essential to determine the average reading in the event that the magnetic field reading varied throughout a region.

### Understanding Magnetic Flux

To calculate the magnetic field, let us consider a magnet’s or a system of magnet’s field-line image represented in the picture below. The plane of the area given by A has a magnetic flux, and it lies in a uniform magnetic field of magnitude B. This magnetic flux is represented by the scalar product of area A and the magnetic field. Here, we need to give importance to the angle at which the field lines pass through the particular surface area. If we imagine a glancing angle at which the field lines cross the area, then

When the angle between the area vector and the magnetic field vector is around 90ᵒ, the flux that results is extremely low.

The resting flux is maximum when this angle is equal to 0ᵒ.

In mathematical terms,

where the angle between vector B and vector A is θ.

Suppose there is a non-uniform magnetic field, and the magnetic field is different in direction and magnitude at different points on the surface. In that case, the total magnetic flux through a particular surface is then given by combining the product of all area elements and the magnetic fields corresponding to them.

### How to measure the Magnetic flux?

Weber (Wb) or Tesla meter square (Tm2) is the SI unit of magnetic flux. It was named after Wilhelm Weber, a German physicist. A magnetometer is an instrument that can be used to measure the magnetic flux. For example, a magnetometer’s probe is moved around an area equal to 0.6 m2 near a huge sheet made of magnetic material and reveals a constant reading of 5 mT. The magnetic flux across that particular area can then be calculated as ( 5 ×10-3 T) ⋅ (0.6 m2 ) = 0.0030 Wb. When the magnetic field over an area is changing, finding the average reading would be necessary.

### Define Magnetic Flux Density or B

B is the force that acts on a wire that lies at 90• or right angles to the field of magnetism per unit current per unit length. Tesla (T) is the unit of magnetic flux density or B. Also, the magnetic flux density is a vector quantity.

### Units of Magnetic Flux Density

The SI and CGS unit of magnetic flux density is represented by the table given below:

 SI unit Tesla (abbreviated as T) CGS unit Gauss (abbreviated as Gs or G)

In 1831, Faraday discovered the phenomenon of magnetic induction, which is one of the greatest milestones in the process of understanding nature at a fundamental level. He found that:

An electromotive force is induced in a circuit by the changing magnetic field in it

The magnitude of this electromotive force is equal to the rate at which the magnetic field flux changes through the circuit.

The flux quantifies how much the magnetic field crosses the circuit. The electromotive force is expressed in terms of volts and is denoted by the formula for the Law of Induction by Faraday:

Here, Φ is the magnetic flux of the vector field B across the circuit, and it is a measure of how much magnetic field passes through the circuit. To understand the concept of flux, imagine a circular ring of area A and how much water from a steady stream of rain will pass through it. If the ring is parallel to the path of the raindroplets, no water goes via the ring. The maximum rate of passage of the rain via the ring is achieved when it is perpendicular to the flow of raindrops.

The rate at which the water drops across the surface is defined as the flux of the vector field pv via that surface. Here p represents the density of the rainwater drops, while v stands for the velocity of these rainwater drops. It is clear that the angle between the surface and v is crucial in determining the amount of flux. A vector A is defined to specify the orientation of the surface so that the magnitude is A (surface area in square meters units) with a direction perpendicular to that of the surface.

The rate of passage of raindrops through the surface is ρv cos θA. Here, θ represents the angle between A and v. Employing the notation for vector; the flux is ρv · A. The amount of magnetic flux through a small area denoted by the vector dA is given by B · dA. If a circuit consists of a single turn of wire, adding contributions from the whole surface surrounded by the wire helps determine the magnetic flux or Φ of the equation.

The induced electromotive force represents the rate of change of flux. Weber is the unit of magnetic flux, in which one Weber is equal to one Tesla per meter square. The negative sign indicates the direction in which there is induction of electromotive force, which is the same as the direction of the current that is induced.

The magnetic flux across the circuit that the induced current generates is towards whatever direction the total flux in the circuit keeps from altering. Also, the negative sign here is an example of the Law of Lens for magnetic systems. This law was deduced by Heinrich Friedrich Lenz, a Russian physicist who states that anything that happens in the system opposes any change in it.

The validity of Faraday’s law is regardless of the process that results in a change in magnetic flux, whether a magnet is moved closer to a circuit or a circuit is moved closer to a magnet. Another alternative is that there may be a change in the size of the circuit in an external magnetic field that is fixed or, as in the case of the generation of alternating current. In this case, the circuit may be a conducting wire coil that rotates in a magnetic field so that the flux alters in time in a sinusoidal way.

In the application of Faraday’s law, the magnetic flux Φ across the circuit has to be carefully considered. Suppose we have a circuit with a coil of five turns that are closely spaced and if the magnetic flux through a single turn is Φ, then its value for the circuit with five turns that is used in Faraday’s law is Φ = 5ϕ. If the five turns are not closely spaced or are not of the same size, it can be quite complex to determine Φ.

### Conclusion

The great insights that Faraday developed from his research helped to find a simple mathematical relationship to describe the set of experiments that he performed on electromagnetic induction. Numerous contributions were made by Faraday to Science. In fact, he was widely recognized in the 19th century as the greatest experimental scientist. Before starting to appreciate his work, you must go about understanding the concept of magnetic flux, as it plays a major role in defining electromagnetic induction.

### 1. What Is the Magnetic Field Outside a Solenoid?

The magnetic field outside a solenoid is zero as there are no magnetic field lines outside it.

### 2. In the Left-hand Thumb Rule, What Does the Forefinger Represent?

In the left-hand thumb rule, the forefinger represents the magnetic field.

### 3. State the Basic Source of Magnetism.

The basic source of magnetism is the movement of charged particles.

### 4. State the Unit of Magnetic Field Strength

The unit of magnetic field strength is A.m-1.

### 5. What Are the Devices That Work on Torque When a Conductor Carrying Current Is Placed in the Magnetic Field?

The devices that work on torque when a conductor carrying current is placed in the magnetic field are the Ammeter, Voltmeter, and Galvanometer.

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