# Velocity gained as a metal object approaches a magnet

I need to find the Kinetic Energy gained as a steel bearing ball approaches a Neodymium magnet. I have the value for the magnetic flux density of the magnet, now I need to find a way to calculate the Kinetic Energy gained by the steel ball as it rolls towards the magnet.

Let's assume that the attraction kicks in at x meters away from the magnet. From that point, the ball accelerates towards the magnet. As it gets closer, the acceleration increases as well.

My first question is, what formulae can I use to find the magnetic attraction between the steel ball and the neodymium magnet of specific dimensions. If it requires more variables than an average student can find out, providing a point of reference or even an online calculator would be greatly appreciated. (ANSWERED)

My second question, how can I find the velocity with which the bearing ball strikes the magnet. As I stated, the acceleration constantly increases as the magnetic forces increase. This leads me to think that there is some calculus involved with the calculations, which isn't a problem. Providing a formula for this or a method to follow would be, again, greatly appreciated.

EDIT: I found a great website for calculating the force a neodymium magnet of specific dimensions applies to a steel surface (https://www.kjmagnetics.com/calculator.asp). I also read about position dependent acceleration, which is the case in my experiment. Now I need to combine these to come up with a final equation.

In a video I watched on position dependent acceleration, this formula is used

\begin{align} a(x) &= \frac{-9.81}{(1+(x/6371))^2} \\\\ \end{align}

This example is based on gravity, but I don't see a reason why it wouldn't work with magnetism. Here, 9.81 is the gravitational acceleration of Earth on its surface, and 6371 is the radius of Earth in kilometers.

If I were to apply this equation to the magnet, I would use the acceleration I derived from the link above as in place of 9.81. Please correct me if I'm wrong, but from my knowledge, the magnet doesn't necessarily has a "center of magnetism", meaning that I don't have to necessarily take the ratio of the distance and the radius (x/6371).

So, I found the answer for my first question, but the second question persists. Any help would be appreciated.

• That equation is strange because $x$ is in kilometres. Commented Sep 8, 2022 at 9:04
• If you know which power is the force with respect to distance ($1/r^4$?) Then you can solve $F=ma$ to get the speed. However note that the problem is harder than that as the magnet accelerates and emits EM radiation losing some of the energy. Commented May 16, 2023 at 18:25
• Or... you could simply measure it. Commented May 16, 2023 at 18:34

I would hook the bearing to a spring with a known spring constant and use that to find the force applied on the bearing. $$F = kx$$ is the spring force equation, where $$x$$ is the distance extended, and $$k$$ is the spring constant