Mathematical relationship between an Ac electromagnet core length, airgap length and flux leakage fa

[obietrice]

Hi,
I recently designed an Ac electromagnet with an airgap length of 80mm having the following design specifications
Core shape - C shape
core dimensions 80mmX80mmX800mm
supply voltage =340Vp
operating freq =50Hz
current drawn =6Amp
number of turns =1024 turns
Magnetic field density B=0.15T
coil wires =AWG 13
Inductance of the coil=127mH

On operating the electromagnet I observed that my the magnetic field density measured at the centre of the airgap was 10 times less than my expected value so was the current but the inductance of the coil increase by a factor of 10.

I have tried investigating the flux loss within the core mean length and observed that the voltage induced on a coil of wire at the center of the core is 10 times lower than that induced in the center of the airgap.

My question? can someone please help me with the mathematical relationship between the core mean lenght, the airgap lenght and flux leakage in an AC electromagnet to help me re-design another core with the same airgap length but with reduce flux leakages within the core length.
An also how I can estimate the temperature rise within the coils and possibly estimate the maximum On and Off time for the electromagnet (duty cycle)
Regards
Obie Trice

 

[obietrice]

The core of the electromagnet was made from silicon steel Grade M4

 

[israelkk]

See the book "Electromagnetic Devices", Roters 1941