Correlation of the Magnetic Field and Magnetic Flux

The magnetic field induction and its correlation with magnetic flux. Magnetic flux is a similar physical quantity in electrostatics that is electric flux.
magnetic flux
Magnetic Field

Magnetic Field

The magnetic flux, its calculation is also the similar phenomena. like we can say in a uniform, magnetic field, through a given area, magnetic flux, can be calculated as, in this situation. We can see if this is a uniform magnetic field of induction b, in which all magnetic lines are parallel and liquid distant. That consider a normal area placed in this region, and the total area is ‘S’ for this section, and find out the total magnetic flux which is passing through this normal area.

Magnetic Flux

Magnetic flux

The magnetic flux phi is equal to BS, because here also we define the magnetic induction as the flux density, so 'B' we can write as phi by ’S’ if phi is the flux passing through it. And if the area is not normal, it is inclined at some angle and we’ll consider it's component. like, say if this is an area which is inclined from the normal direction to magnetic field by an angle theta. It is said this area is 'S', then we can say, we resolve it in 2 perpendicular components.  If this area is ‘S’ this area will be S sine-theta and, the area which is normal to the direction of magnetic field. The component of this area which is normal to the magnetic field is 'S' cos-theta.
Magnetic Field

Electric-flux

So in this situation, we can say, whatever flux is passing through in this area, 'S' cos-theta will be passing through the total area. Its area vector we can say from which the flux is coming out is normal to the surface, this is s vector and this is the direction of magnetic induction vector. The angle between the 2 is also theta. So here we can write magnetic flux through this area phi is equal to BS cos-theta. Because the flux density or magnetic induction is the flux per unit normal area. In this situation this flux we can write as, B dot S, which is almost the similar way, which we’ve already applied in the calculation of electric flux, that if electric field strength is e through a given area, the electric- flux is B dot S in a uniform electric field. Similar to that here if magnetic induction is non- uniform, we can calculate magnetic flux,


Magnetic induction
The non-uniform magnetic induction, we can say in a non-uniform field, if we talk about the magnetic flux, this is the magnetic induction B vector which is not uniform in this region it is varying. The flux density is different at different points. And here if we consider a given area. It's considered a small elemental area DS over here. The direction of DS vector will be normal to this bed S vector at this point. The direction of magnetic induction will be tangential to any magnetic line passing through DS. If this angle is theta, here we can write let D phi, be the magnetic flux, through elemental area DS. This implies we can write D phi is equal to B dot DS.

Because of the elemental area DS, we can consider B is not varying in such a small region. It can be written as BDS cos-theta. And we can calculate the total flux, through a surface, by integrating this value like here phi will be the integration of D phi. That’ll be an integration of B dot DS, or it is an integration of B DS cos-theta. The limit will be for the surface M if we name the surface as 'M'. Here we should always keep in mind that in a non-uniform field, flux can be calculated by using the expression integration of B dot 'DS'. And if the field is uniform that can be directly calculated by integration of 'B' dot 'S'.

There is I explained above the correlation with magnetic flux and Magnetic flux.

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