Calculating flux density in an air gap

[escape_velocity]

I am trying to calculate the flux density of an air gap in an electromagnet.
I am following this page that calculates the flux density in a C core with an air gap.

My confusion is that I am using 50Hz AC instead of DC I have control over the voltage amplitude since I would be using a variac to do my initial tests.

Would the calculations differ for AC, my guess is that it would be different since the AC impedance of the coil would come into play and that would change the MMF(magneto-motive force) value.

I have a C core of Electrical steel (laminated) with the following parameters
Permeabity of core = 5.0×10⁻³ H/m
Cross section Area = 1cm²
Magnetic Path Length = 19cm
Air Gap length = 1cm
Flux Density needed in air gap = 1Tesla

Would appreciate your thoughts on how to go about doing this calculation.
Thanks in advance.

 

[Hesch]

My confusion is that I am using 50Hz AC instead of DC

Well, if you use a sinusoidal AC current, you will get a sinusoidal flux. The flux density is proportional to the current.

So is the needed flux density ( 1T ) the peak value, the RMS value or . . . ?

I suggest that you calculate the DC current at first. You should find the result as: amps⋅windings. The AC impedance depends on the number of windings ( and on the resistance of the windings ). Knowing the impedance and the needed current, you can calculate the AC voltage needed.