Is the magnetic flux density B constant?

[J Silva]

Summary:: Is the magnetic flux density B constant? Is the magnetic flux constant?

I am working on a project design for Uni and I am stuck.

In a magnetic circuit is either the magnetic flux or the magnetic flux density B constant? This magnetic circuit has all different cross section areas and air gaps.

I need to calculate the Magnetic Force generated by the circuit and also N*i= Φ1 * R1 + ... (N beeing nº of spirals in a coil and R the reluctance).

I am stuck in a loop because I think neither B nor Φ are constant.
I was told to use saturation flux density (Bsat=2.13) of the material to jump start the calculations, but I am stuck on the question at hand.

Any insight would be appreciated and sorry for the lack of understanding in electromagnetism.

 

[J Silva]

I am working on a project design for Uni and I am stuck.

In a magnetic circuit is either the magnetic flux or the magnetic flux density B constant? This magnetic circuit has all different cross section areas and air gaps. I need to calculate the Magnetic Force generated by the circuit and also N*i= Φ1 * R1 + ... (N beeing nº of spirals in a coil and R the reluctance). I am stuck in a loop because I think neither B nor Φ are constant.

I was told to use saturation flux density (Bsat=2.13) of the material to jump start the calculations, but I am stuck on the question at hand. Any insight would be appreciated and sorry for the lack of understanding in electromagnetism.

This circuit is for an eletromagnetic brake. I have all of the dimensions and reluctances. I also have an estimated current and Number of spires that depending on the results of the question I will have to revise in order too see if they are appropriate. The final objective is for the magnetic force to be equal or larger than a known value.

 

[Gordianus]

I guess you're assuming the core is of a high permmeability material and that the gap is small enough as to make "fringing" negligible. In such a case the $\vec B$ field lines follow the shape of the core (no field outside the core or the gap). Thus, considering$\oint{\vec B \cdot d\vec S}=0$ we get $B_1S_1=B_2S_2$ (I skipped several intermediate steps)

 

[J Silva]

I guess you're assuming the core is of a high permmeability material and that the gap is small enough as to make "fringing" negligible. In such a case the $\vec B$ field lines follow the shape of the core (no field outside the core or the gap). Thus, considering$\oint{\vec B \cdot d\vec S}=0$ we get $B_1S_1=B_2S_2$ (I skipped several intermediate steps)

Could I then assume that Bsat (saturation flux density) is the value of flux density that is applied to the smallest cross section (S) ?

 

[Gordianus]

Your drawing shows an axisymmetric core (is that O.K.?) but without dimensions. Anyway, I suppose the smallest cross section is around the central "hole". That section shouldn't reach the saturation point of 2. 13 T.

 

[J Silva]

Your drawing shows an axisymmetric core (is that O.K.?) but without dimensions. Anyway, I suppose the smallest cross section is around the central "hole". That section shouldn't reach the saturation point of 2. 13 T.

The core is a cylinder (9) with a coil runing through it (8). The sallest section are would be the one I painted red and with the arrow in the picture bellow.
I was thinking of considering B a percentage o Bsat, such as B = 70% Bsat

 

[Gordianus]

The force you get goes as the square of B. Thus, working at 70% of Bsat you'll get half the maximum one.