Force exerted by Ferro-magnetic Electromagnet

[Nythe]

I've been confused for awhile about this and I haven't found any decent explanatory answers.
I read somewhere that the general formula for finding the force exerted by a solenoid electromagnet could be found by:

Force = ((N x I)^2 x k x A) / (2 x s^2)

where N is number of turns of a coil,
I is the current passing through the coil,
A is cross-sectional area of the solenoid,
s is distance between solenoid and external object,
k is permeability constant (4 x PI x 10^-7)

Which part of this formula takes into account the inherent magnetic strength of the solenoid? I mean, wouldn't there be a difference in the force exerted if the solenoid was ferromagnetic instead of non-ferromagnetic? Because I also read that a ferromagnetic core like soft iron would amplify the magnetic strength of the electromagnet several hundreds even thousands of times.
So how could I find the force that an iron core electromagnetic would exert using this formula? Thanks for any help..

 

[gabbagabbahey]

I read somewhere that the general formula for finding the force exerted by a solenoid electromagnet could be found by:

Force = ((N x I)^2 x k x A) / (2 x s^2)

The force exerted on what?

Which part of this formula takes into account the inherent magnetic strength of the solenoid? I mean, wouldn't there be a difference in the force exerted if the solenoid was ferromagnetic instead of non-ferromagnetic? Because I also read that a ferromagnetic core like soft iron would amplify the magnetic strength of the electromagnet several hundreds even thousands of times.
So how could I find the force that an iron core electromagnetic would exert using this formula? Thanks for any help..

The magnetic field of a solenoid electromagnetic, along its axis, outside the solenoid, is proportional to to NI/s and can be found from the Biot-Savart Law.