# Strength of an electromagnet

1. Apr 24, 2008

### Nabeshin

So, I'm playing around with electromagnets right now and I was wondering how to calculate (or determine experimentally) the approximate strength of the electromagnet. What I'm doing right now is using the formula for a solenoid, $$B=\mu_o N i$$ and adding the constant for whatever material is in the center (iron right now, so x200). The thing is, for the magnet I have sitting in my room right now I have i>.250mA (highest rating my multimeter goes to) which is giving me a magnetic field strength of 1.13T. So, this is kind of ridiculous and I don't think this is what I'm really getting so here lies the problem:

Because I wrapped the wire around multiple times, does the distance from the iron core factor into the equation? It makes sense to me that each successive wrap will have less effect than the previous one. Also, I don't mind experimentally determining the value, but I'd like to have it in Tesla. Any idea how to convert data if I lift, say, a .5kg object into a tesla value at the surface of the magnet? Thanks for any help provided!

2. Apr 25, 2008

### pam

In gaussian units, $$F=2\pi M^2A$$ is the lifting force, where M is the "magnetization" of the magnet and A is the common contact area in cm.
With iron in contact, $$B=4\pi M$$ (in gauss) at the end of the magnet.
If iron is not in contact, B at the end is $$2\pi M$$.

3. May 9, 2008

### yomega

I got this equation from a few friends and to be honest i dont even fully understand it myself yet but i hope it helps

1. The force generated by an electromagnet is approximately:
F = mu_r^2 * mu_o * N^2 * I^2 * A / (2 * L^2), where
mu_r is relative magnetic permeability of the magnet core.
mu_o is the permeability of freespace (4*pi* 10^-7)
N is the number of turns of wire in the magnet coil
I is the current in the coil, in amperes
A is the cross-sectional area of the core (in m^2)
L is the magnetic circuit length, including the object being lifted.

2. Since most iron saturates at about 1-2 Tesla, you have to check the field strength with this formula:
B = mu_r * mu_o * N * I / L, in Teslas