OK.
A solenoid with a current i and n loops is placed on a ramp inclined at an angle theta to the horizontal. Consider the magnetic field of the earth and calculate the acceleration of the solenoid down the slope in respect to position.
(You'll need to introduce a few basic constants with the algebra)
Edit: To make life easier and to simplify the maths, presume that the solenoid can immediately roll without slipping.
Been a while since I've done (few) umep problems, hope it's close
If we assume the magnetic field is perpendicular to the direction of the slope. The current will not affect the acceleration due to the right hand slap rule cancelling out over the circular loops. The problem is then reduced to a rolling tube.
The same thing happens if the magnetic field is parallel to the slope.
Take the contact point between the solenoid and the ramp to be the pivot.
By the parallel-axis theorem
(I know this solution probably isn't what you had in mind and I might have misunderstood but oh well...
In the meantime, have a go at this problem. I hope it isn't pushing the math limits, but it is a variation on a classic electromagnetism problem.
We have a line of positive charge of length L and total charge Q. At one end, a certain distance 'z' (or call it whatever you like)
above the line of charge is a point P. Find the Electric field at that point. Express it in terms of vectors in the x and y directions.)
[There are several ways to get the answer]