Magnetic Force Applied to An Object @ d (0,n) (Rail gun on Mars)

[Rra]

So long story short, I'm trying to write a scientifically accurate short story/animation thing and it revolves around a mass driver: it's a giant and deep hole on Mars with a magnet on the bottom or sides or something and fires packets of objects to Earth at breathtaking speeds (4.66 million meters per second, to be exact, which will take on average 13.4 hours to travel).

Okay, none of that was relevant to my question...

What is the equation for force acted upon an object based on the distance between the object and a magnet?

I'm sure there's more variables than just f and d, but I'm totally lost on the physics of magnets.

You won't hurt my feelings being harsh, just please be proactive. Thanks!

 

[Evo]

I have moved your thread to the writing forum.

 

[stefan r]

So long story short, I'm trying to write a scientifically accurate short story/animation thing and it revolves around a mass driver: it's a giant and deep hole on Mars with a magnet on the bottom or sides or something and fires packets of objects to Earth at breathtaking speeds (4.66 million meters per second, to be exact, which will take on average 13.4 hours to travel).

Okay, none of that was relevant to my question...

What is the equation for force acted upon an object based on the distance between the object and a magnet?

I'm sure there's more variables than just f and d, but I'm totally lost on the physics of magnets.

You won't hurt my feelings being harsh, just please be proactive. Thanks!

Magnet

the magnetic field near either end falls off inversely with the square of the distance from that pole.

Gravity is also inverse square of distance.

I believe that in a rail gun the barrel is inside of the magnet. So just use the magnetic field strength.

You might be looking for armature.
So

I is current, l is armature length B is the magnets.

Why in a hole on Mars? Launching from Deimos there is no atmosphere vaporize the object. There is magma inside of Mars so you can not make the barrel long enough to reach that velocity with any existing technology.