# How to calculate acceleration of ball bearing due to magnet

I have an 50N cylindrical electromagnet, which is about 25mm in diameter and 20mm heigh, under 1mm of plastic. Running directly on-top of the magnet is a straight track along with a 10mm in diameter steel ball bearing rolls.

While the ball bearing is rolling toward the electromagnet, it's turned on, and is turned off when the ball bearing is exactly on top of it.

If I know the ball bearing's initial velocity, how do I calculate the final velocity of the ball bearing when it's directly over the electromagnet, after having gone through acceleration due to magnetic pull?

I've Googled the basic formulas for magnetic pull in free space, but they all seem to refer to variables I don't know, such as magnetic flux or the number of turns in the winding.

• you will probably need some electronic circuitry to sense when the ball-bearing is close That's exactly what I'm doing. I have a sensor that measures the velocity of the ball about 3 cm away from the center of the magnet. However, for my application, I can't put a sensor directly at the magnet, so I have to calculate when the ball bearing is directly on top of it using velocity, distance and time. Therefore, I need to calculate acceleration due to the changing force magnet. I thought it would be a simple squared-dropoff formula like other EM fields or gravity. – Cerin Jul 31 '17 at 21:10