Force exerted by Ferro-magnetic Electromagnet

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..

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 Quote by Nythe 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.

 Tags electromagnetic, ferro, force