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.


This is not something which is easy to calculate. Some things are much easier to find out by experiment or measurement, rather than by calculation.

The magnetic field is quite weak outside of the solenoid. It is strongest inside, on the axis. It would be more effective to run the ball-bearing along the axis of the electromagnet.

If you expect to increase the speed of the ball-bearing significantly, you will probably need some electronic circuitry to sense when the ball-bearing is close the the point at which the force on it changes direction and automatically switch off the solenoid.

  • $\begingroup$ 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. $\endgroup$ – Cerin Jul 31 '17 at 21:10
  • $\begingroup$ When I've estimated that the ball is directly on top of the magnet, I using a transistor to deactivate the electromagnet, allowing the ball to continue at an accelerated rate. Currently, I'm having trouble accurately timing this event, because I don't know how to calculate the acceleration due to the magnet. $\endgroup$ – Cerin Jul 31 '17 at 21:12
  • $\begingroup$ The ball-bearing interrupts the light beam of the sensor. The electronics (transmitter and receiver) can be quite far from the electromagnet. ... Alternatively, with your present apparatus, you could experiment with a fixed velocity at the sensor, adjusting the delay to switch-off until you find the maximum boost to the speed. Repeat for different speeds at the sensor, plot the results (ie input speed vs optimum delay), then interpolate to get an approximate formula. $\endgroup$ – sammy gerbil Jul 31 '17 at 21:53

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