I would like to create a basic electromagnetism simulation in blender; just two separate coils attracting each other (they slide and touch).
I'm good for modelling this, just not sure how to set up the physics.
This can be modeled using blender physics. The animation was generated in Blender 2.76b from the attached .blend file. It uses the built-in physics. It shows attraction (blue-red), followed by repulsion (red-red).
A blender file illustrating this approach:
This solution is similar to the approach described in this question: How to have rigid-bodies and charge fields interact?
I'd suggest using the Limit Distance Constraint. You can set it up reciprocally on both coils (each one set up with the other coil as the target object).
By animating the Distance value you can visualize magnetic attraction between the two objects.
If your unfamiliar with constraints, this is a good intro. To add a Limit Distance constraint, select your object, then go to the Constraints (chain icon) tab in the Properties Window, then: Add Object Constraint > Transform > Limit Distance.