Magnetic Flux And Area: 7 Important Facts You Should Know

The magnetic fluxes are the imaginary lines penetrating through the material when kept in the electromagnetic or magnetic field. The magnetic flux and area are interdependent.

The magnetic flux and the field strength depend upon the area of the conducting material and are linearly dependent on the area. As the area of the conducting material increases, the magnetic flux through the conductor also increases.

How is magnetic flux related to area?

The magnetic flux through the material kept in the field will be more if the area of the conductor is more.

The magnetic flux penetrating through the conducting material will increase if the area of the material kept in a field is more. Hence, the magnetic flux is directly proportional to the area of the material along with the magnetic field.

The magnetic field is directly related to the area of the conductor by the relation,

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Here, A is the area through which the magnetic field lines are penetrating, B is a magnetic field and θ is the angle made between the magnetic field direction and the magnetic flux lines.

Does magnetic flux depend on area?

The magnetic flux does depend on area as the flux through the material increases if the area of the material is more.

The magnetic flux is a very essential concept to determine the net magnetic flux through the material and it directly depends upon the area. The larger the area of the conductor, the more of the flux will be allowed to penetrate through the material.

How to find magnetic flux from area?

The magnetic flux is the integral of the magnetic field in a unit area.

The magnetic flux from the area can be found by knowing the intensity of the magnetic field in the region and the total area of the conductor. The magnetic flux through this conductor is the product of this both.

Consider a plane conducting area in the magnetic field region. Let da be the small element having a surface area of one meter square. The total magnetic field lines dφ are penetrating through this small element da in the direction making an angle θ as shown in the figure below.

image 36
Magnetic flux through the unit area

The magnetic flux passing through the unit area is the integral multiple of the magnetic field in the region and the area da under consideration. Hence, the magnetic flux is given by the relation,

The magnetic field is a common term as it is not variable in this situation, hence we can rewrite the above equation as,

The integral of da is the total area of the material in the magnetic field. Solving the integral, we get:

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Here, θ is the angle made by the magnetic field lines with the direction of the field.

If the field lines are perpendicular to the magnetic field direction, then θ=0 and hence, we get the above expression as,

φ=BA

The magnetic field is the product of the magnetic field produced and the area of the conductor through which the magnetic field lines are penetrating. This equation gives the relation between the magnetic flux and the area.

How does magnetic flux change with area?

The magnetic field varies with the area of the magnetizing material.

Since magnetic flux is directly dependent on the area of the conducting material in the field, the magnetic field will decrease if the configuration of the material is decreased and increases if the area of the conducting material is increased.

The magnetic field strength increases if the magnetic flux penetrating through per unit area of the material increases. It clearly depends upon the type of magnetic material kept in a field. The ferromagnetic material will allow more magnetic flux through the material as the magnetic dipoles are easily arranged in the magnetic field direction.

How to find the area of a magnetic flux?

The area of the magnetic flux is the total area of material through which the magnetic flux penetrates.

The area of magnetic flux is the ratio of the magnetic flux through the area divided by the total magnetic field. The area of magnetic flux can also be calculated from the magnetic flux flowing through the material divided by the density of the magnetic flux through a unit area.

We know that the density of the magnetic flux is the total number of the magnetic field lines moving across the unit area of the conductor. That is given by the formula,

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Here,

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is the density of the magnetic flux through a unit area, φ is the magnetic flux, and A is the area of the material.

Hence, the area can be calculated if we know the density of the magnetic flux in a unit area and the net flux through the material by modifying the above formula as,

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The area of the magnetic flux is the ratio of the magnetic flux and the density of the magnetic flux through the unit area.

Magnetic Flux vs Area Graph

The magnetic flux is directly proportional to the area of the material and hence, as the area of the material increases, the magnetic flux has to increase. The greater the area, the more will be the magnetic flux penetrates through the material.

Hence, the magnetic flux versus area graph looks like as shown below:

image 37
The graph of magnetic flux v/s area

The graph clearly shows the relation between the magnetic flux and the area. As the area of the magnetizing material is more, then it will allow more and more magnetic flux to penetrate through it. And hence the magnetic flux through the material will increase.

The magnetic field density will not change with enlarging the area of the material. The magnetic flux density for a particular material producing a fixed magnetic field will remain constant. Whereas the magnetic flux entering through the material will vary.

Suppose the magnetic field produced by a certain magnetizing material is 2T. The different plane sheets of the variable areas of the same material are kept in the same electromagnetic region, and the magnetic flux through the material is calculated. It was found that the magnetic flux lines remain parallel to the direction of the magnetic field.

The following data was noted,

Area (m2)Magnetic Flux (Wb)
12
24
36
48
510
Table: Variation in magnetic flux with different areas of the conductor

Let us plot the graph of magnetic flux v/s area using the above data now, and understand the concept.

magnetic flux and area
The graph of magnetic flux and area

Here, is a graph of magnetic flux and the area of each plane sheet kept in the magnetic field region. The graph depicts that the magnetic flux linearly increases with the area. With the increasing intensity of the magnetic field, the total number of flux penetrating through the area intensifies.

How much is the magnetic flux through the unit area of the conductor if the magnetic field is B0a2? Note that, a is the area and B0 is the initial magnetic field?

Given: B=B0a2

A=1m2

The magnetic flux through the unit area can be calculated using the expression,

Substituting the value of B in the expression, we get:

Taking the common term out from the integral, we have,

Solving the above integral we get:

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Substituting the value for area, we get:

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Hence, the magnetic flux is one-third of the initial magnetic field.

What is the magnetic field if the magnetic flux flowing through the area of 0.16 m2 is 1 Wb?

Given: A = 0.16 m2

φ =1 Wb

The magnetic flux is related to the magnetic field by the equation,

φ =BA

Here, φ is the magnetic flux, A is the area, and B is the magnetic flux.

Hence, the expression to calculate the magnetic field from the magnetic flux is,

B=φ/A

Substituting the values in this expression, we get:

Solving this further, we get:

B=6.25 T

Hence, the magnetic field in which the material is kept is 6.25 T.

Conclusion

The magnetic flux is directly dependent on the area of the magnetizing material. The total number of magnetic flux entering the conductor at a constant magnetic field varies with its area. If the surface area of the conductor is enlarged then the magnetic flux will increase through the conductor. The magnetic flux linearly increases with the area.

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