electromagnetism - Magnetic Force on a Ferromagenetic Material

I am currently working on a project involving solenoids, and I needed a force(Newtons, not a measure of magnetic field strength) equation. What I came up with after some digging around on the internet, is the equation:

$$F = (NI)\mu_0\frac{\text{Area}}{2g^2}$$

Where $F$ is force (in Newtons), $N$ is the number of turns in the coil, $I$ is the current being passed through the coil, $μ_0$ is the magnetic permeability of vacuum, and $g$ is the gap between the coil and the ferromagnetic material. (Area $A$ and $g$ can be any units, as long as you're consistent with the usage)

I don't know in which plane exactly the area $A$ is taken.

Assuming I have a rod, moving lengthwise into a solenoid, which plane would $A$ represent?

Plane a, plane b, or another plane that I did not consider relevant to this problem?

Rod:

Edit: I was looking for the force an electromagnet would exert on a ferromagnetic material moving into the coil. something like this.

Edit: If the equation I was using before does not work, I don't suppose anyone has the correct one?

Edit: After looking at the equation some more, I realized I had written it wrong. It should be:

$$F = (NI)^2\mu_0\frac{\text{Area}}{2g^2}$$