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# Magnetic Flux

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Last updated date: 23rd Jul 2024
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## Magnetic Flux - Formula, SI Unit & CGS Unit

A sub-discipline of physics in the field of electromagnetism is the magnetic flux through a surface, which refers to the surface integral of the magnetic field's (B) normal component passing through that surface. To be specific, magnetic flux is defined as the number of magnetic field lines passing through a given closed surface. In this particular scenario, the area under consideration can be in any orientation corresponding to the direction of the magnetic field and of any size.

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### Symbol and Formula of Magnetic Flux

Magnetic flux are denoted by the Greek letter Phi and have the symbol \[\Phi  or \Phi _{B}\].

To calculate the magnetic flux, we can use the formula given below:

\[ \Phi _{B} = B. A = B A cos \Phi \]

Where,

\[ \Phi _{B} \]  = Magnetic Flux

B = Magnetic Field

A = Area

\[ \Phi \] = Angle at which the magnetic field lines pass through the given surface area

Fluxmeter is used to measure the magnetic flux.

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### SI Unit of Magnetic Flux

Weber (Wb) is the SI unit of magnetic flux, which is named after Wilhelm Eduard Weber, a German physicist. A flux density of one Weber per square meter or \[Wb/m^{2}\] is one Tesla, denoted by T (explained in the next section). Quite often, Weber is expressed in a multitude of other units, as shown below:

\[Wb = kg m^{2}/s^{2} A = V.s = H.A = T.m^{2} = J/A = 10^{8}Mx\]

Where, Wb = Weber, T = Tesla, V = volt, m = metre, J = joule, s = second, H = Henry, A = ampere, and Mx = Maxwell.

### CGS unit of Magnetic Flux

The CGS unit of magnetic flux is Maxwell (Mx) or Abweber (abWb).

### Fundamental Unit of Magnetic Flux

The fundamental unit of magnetic flux is Volt-seconds.

### Understanding the Term Magnetic Flux Density

The force acting per unit length on a wire placed perpendicular (at right angles) to the magnetic field per unit current is the magnetic flux density (B).

•  Tesla (T) or \[ Kg s^{-2} A^{-1}\] is the SI unit of magnetic flux density (B).

•  The magnetic flux density, denoted by the symbol B, is a vector quantity

• The CGS unit of magnetic flux density is Gauss, which is abbreviated as G or Gs

The formula for calculating the magnetic flux density is as follows:

B = F/I L

Where

F = total force acting on the wire

I = current flowing through the wire

L = length of the wire

### Submultiples of Weber(Wb)

 Value SI Symbol Name 10-1 Wb dWb deciweber 10-2 Wb cWb centiweber 10-3 Wb mWb milliweber 10-6 Wb µWb microweber 10-9 Wb nWb nanoweber 10-12 Wb pWb pico weber 10-15 Wb fWb femto weber 10-18 Wb aWb attoweber 10-21 Wb zWb zepto weber 10-24 Wb yWb yocto weber

### Multiples of Weber

 Value SI Symbol Name 101 Wb daWb decaweber 102 Wb hWb hector weber 103 Wb kWb kiloweber 106 Wb MWb mega weber 109 Wb GWb gigaweber 1012 Wb TWb teraweber 1015 Wb PWb Peta weber 1018 Wb EWb exaweber 1021 Wb ZWb zettaweber 1024 Wb YWb yotta weber

### Magnetic Flux

It can be defined as the total number of magnetic field lines which pass through a given closed surface. This quantity provides a measurement for the total magnetic field in a given area. The areas we take into consideration are of different sizes and different orientations considering the magnetic field direction. It is generally measured using a flux meter. There are different units for flux. In the SI unit, it is Weber which is abbreviated as Wb. The CGS unit that is used for this is Maxwell and the unit used fundamentally is Volt-Seconds. Thus, it is a measurement of the total magnetic field that passes through an area we take into consideration. It is a very good tool that can be used for finding the magnetic force on an area. It is related to the area chosen and we can choose an area of any size and arrange it according to the magnetic field.

Faraday conducted his experiment on electromagnetic induction and gave insights on the mathematical relation related to it. He made many contributions to science and was known greatly in the \[19^{th}\] century for his scientific contributions. Magnetic flux plays a major role in the process of electromagnetic induction. In order to calculate this quantity, we take into consideration the field-line image of a magnet or many magnets present.

## FAQs on Magnetic Flux

1. Why is the magnetic flux in a closed surface?

Magnetic flux can occur in both open and closed surfaces and it is zero when it goes through a closed surface. It cannot be zero when there is an open surface and thus, it is a very important quantity in the field of electromagnetism. When we consider the flux present on a surface then we consider the boundaries of the surface taken into consideration. The actual shape is not relevant and the integral of any surface that has the same boundary is equal. This is because the flux is zero when we consider a closed surface.

2. What are the properties of magnetic flux?

The following are the properties of the magnetic flux:

• It forms a loop that is closed.

• It always starts from the North Pole and ends in the South Pole.

• These quantities never intersect one another.

• The lines of magnetic forces which are parallel to each other and present in the same direction repels each other.

3. What is the difference between magnetic flux and magnetic field?

The main difference between these two quantities is that the region around the magnet where force is experienced by the charge moving around it is called the magnetic field. On the other hand, the strength or quantity of the magnetic lines of forces produced by the magnet is called the flux. Both these are magnet properties. Magnetic field is thus the area where force is experienced by a moving charge and magnetic flux represents the magnetic lines which pass through that area. We can determine the presence of a magnetic field by placing a magnetic needle around an area.

4. What is the difference between an electric circuit and magnetic circuit?

There are many differences between these two quantities. The magnetic circuit occurs as a closed path for magnetic flux whereas the electric circuit occurs for electric current as a closed path. The unit for magnetic circuit i.e. flux is expressed as Weber or Wb whereas for electric circuit, it is amperes. In a magnetic circuit, the driving force is the magnetomotive force and is measured in ampere turns. On the other hand, the driving force for an electric circuit is electromotive force which is expressed in volts. Reluctance is the force that opposes the magnetic flux flow in the magnetic circuit. In an electric circuit, the force that opposes the flow of current is named as resistance.

5. What is the difference between magnetic and electric fields?

The difference between magnetic and electric field are as follows:

• Electric field is the area around where force is experienced by a moving charge. Whereas, the area around the magnet where there is a force of attraction or repulsion near the magnetic poles is called the magnetic field.

• The SI unit for both these quantities are different. For electric field, it is Newton/Coulomb and for magnetic field it is tesla.

• Both these quantities are vector fields or quantities.

• The intensity of the electric field is measured using an electrometer but a magnetometer is used for measuring the intensity of the magnetic field.