Dimensional Formula of Magnetic Flux

In electromagnetism, there were many experiments or theories proposed by physicists. In those theories, magnetic flux takes an important place. The electromagnetic induction is explained via the current concept. When we are changing the magnetic fields, there would be a generation of electric current in a coil. Most of the experiments related to electromagnetism were done by Henry and Faraday. We can discuss the overview of magnetic flux with the dimensional Formula of magnetic flux. The dimensional Formula of magnetic flux is derived with the help of a magnetic field. The magnetic flux importance is also explained. 

Magnetic Flux

In general, if an electric charge (e–) is mobile in any space, its movement of force is measured in two quantities, namely, electric force and vector. The electric force is not related to charging velocity but depicts only the charge component. The vector is nothing but the magnetic field generated when the charge moves. The amount of vector or magnetic field passing into the unit area is termed magnetic flux.

Overview 

The magnetic flux can be used to measure the magnetic field in both the flat surface and closed surface. It can be of any size and orientation. The unit is tesla or weber per m2. It can be written as B  = B .A . 

Dimensional Formula of Magnetic Flux

The magnetic field is formulated as B = force / (charge x velocity) .

Let us take the dimensions of each term in the formula separately and derive the dimensional formula.

For force, it is [ M1L1T-2].  

[ I1 T1 ] is for the charge, and [ L1T-1] is for the velocity.

B =    [ M1L1T-2] / [ I1 T1 ]  [ L1T-1]

So, the dimensional formula of magnetic field (B) =  [M1T-2I-1 ]

We already know that ( B ) = B A

Here, Area (A) = [L2] and we have already calculated for B.

Let’s substitute the dimensions,    =  [M1T-2I-1 ] [L2]

   =  [M1L2T-2I-1 ]

The dimensional formula can be written as [M1L2T-2I-1 ]. 

Derivation 

As we have already seen that it is formulated as

B  = B .A   

B  = B . A. cos

B  = A [ B cos ]

Here,

  B  = magnetic flux

= angle between B and A   

In case, we are taking  cos = 0 , = 900

is at normal here, and we have a parallel vector B .

Hence, it can be formulated as  B  = B . A. 0

  B  = 0

The magnetic flux is equal to 0.

Let us consider cos = 1, = 00

Take  B  perpendicular to the surface, then

B = .H

In the above equation, = permeability 

H = magnetic intensity

H is the number of lines in the unit area. 

Since  B is perpendicular to the surface, the magnetic flux would be maximum and non-uniform.

It can be defined as below,

d B  = B . ds

d B   =  B . nds

The above magnetic field is measured for only small area ds. This can also be written as

B   =  ∲ B . nds

∲ is the surface integral of flux through a surface.

Importance

The magnetic flux can be used to determine the magnetic field on a surface. Faraday’s law describes the rotation of the magnetic field in the coils. It results in a change in flux. So, the generated voltage can be measured easily.

The Gauss law of magnetism is used to study the reaction of magnetic flux in closed surfaces. We all will be aware that the magnet has dipoles in it, but on a closed surface (like a sphere), there won’t be two poles. So, the magnetic flux is equal to zero.

It describes the effect of magnetic force in an area. 

Dimensional Formula

The physical quantity’s dimensions are the powers to which the basic quantities are elevated to represent that amount. The dimensional formula of any physical quantity is an equation that explains how and which of the base quantities are contained in that amount. It is written by enclosing the symbols representing base amounts in square brackets with the corresponding power, i.e. ().

E.g.: the dimension formula of displacement is: (L)

A dimensional equation is obtained by equating a physical quantity with its dimensional formula is used to calculate the dimensional equation of any physical quantity.

Conclusion

We have discussed the overview of magnetic flux with its derivation. The amount of vector or magnetic field, passing into the unit area is termed magnetic flux. The unit is Weber per m2. The Dimensional Formula of Magnetic Flux is derived by using the standard physical quantities and magnetic field. The determination of the magnetic field on a flat and closed surface depicts the magnetic flux importance. For this, Gauss’ law of magnetism and Faraday’s law help a lot.