# Equations for finding magnetic force between magnet and solenoid

1. Jul 4, 2014

### samman010

Hi everyone.

I was doing an experiment on the effects of varying the distance between the solenoid and magnet, the voltage across the solenoid, and temperature of the iron core inside the solenoid on the magnetic field produced and the magnetic repulsion between the solenoid and magnet.

The magnet was placed on a scale with blu-tack and the solenoid with the iron core was placed above with a retort stand. Those variables were then changed one at a time.

My question is, how do I find the theoretical force of repulsion between the magnet and solenoid? I already have the readings (tared). I have found some equations, however I lack information on the iron core and do not know how much it affects the magnet field. What is its permeability? I read that it varies.

I have found this formula for finding the force:

$F=\frac{\mu_{0}m_{1}m_{2}}{4\pi r^2}$

And also for finding the magnetic pole strength:

$m=\frac{NIA}{L}$

But since I have an iron core, wouldn't that affect magnet pole strength? It only has number of turns, current, area and length in the equation.

Also how would I find the magnetic pole strength of the permanent bar magnet that I used?

Thank you.

2. Jul 4, 2014

### Staff: Mentor

In general, that's a complicated problem, especially if coil and magnet are close to each othe (compared to their size).

Where does that formula come from?

For an iron core, multiply it with µr, if the result is small compared to the saturation field of iron (~1-2 Tesla). If it is not, it gets more complicated.

With data points of your coil, or with a magnetometer (magnetic field strength sensor).

3. Jul 5, 2014

4. Jul 5, 2014

### samman010

Also, how would the permeability of the iron core change with temperature? Are there any equations?

5. Jul 5, 2014

### Staff: Mentor

That equation looks odd. It does not give the right units, and the force should drop with the 4th power of the distance, not with the second power.

I'm sure there are tables, but I don't know where.

What is the scope of this experiment?