# Figuring out the effective pulling distance of an electromagnet

1. Aug 10, 2008

### Summit07

Hey Everyone,
So here is my situation. I have a PVC tube six feet long, with electromagnets placed at either end. In between the electromagnets is a steel disk. The electromagnets I have been researching are anywhere from 1in to 12in in diameter with breakaway strength of 14lbs to 3500lbs. What I am looking for is how powerful the electromagnets would need to be in order to attract the steel disk from six feet away. Any help in figuring out the effective pulling distance of an electromagnet would be greatly appreciated. Thank you!
Sincerely,
Chris

2. Aug 10, 2008

### Phrak

At distances that are large compared to the dimensions of the magnet, the magnetic field stength is proportional to the inverse cube of the distance.

http://en.wikipedia.org/wiki/Magnet" [Broken]

Apparently you're set up to take some measurements. Using dimensional analysis you can infer the force produced by the larger magnets by measurements on the smaller.

Are your large and small magnets similarly shaped, and can you measure the force between the steel and magnets when they are separated?

Last edited by a moderator: May 3, 2017
3. Aug 10, 2008

### Summit07

Thank you Phrak for the great advice! I will being working on the distance problem using the information you supplied. The strengths and dimensions I listed were from several manufacturers of electromagnets that I am interested in buying. I don't actually have any of the magnets on hand. Could I still use the distance information you listed to figure out the force between the two magnets?

4. Aug 10, 2008

### Phrak

You're welcome :)

I won't attempt to paraphrase what is well written in the Wikipedia article. If you click the link and word-search on "distance" you should get the general idea.

5. Aug 10, 2008

### Summit07

Hey Phrak,
I have been researching the wikipedia articles you have pointed out and several others. I am using the equation of F={{\mu q_{m1} q_{m2}}\over{4\pi r^2}}. It is show better in the article obviously. What I am having trouble with is finding the magnitudes of the poles. I have found that permeability is equal to magnetic field B / magnetic field H, but I am a little confused on that as well.

6. Aug 10, 2008

### Summit07

One more thing. Once I have found the force of the magnets could I plug it into this equation as listed in the wikipedia article? The equation is this, or at leas I think. Strength of the magnet divided by the distance from the magnet's center cubed. The answer to that equation would give me how strong the force is of the magnet. Is that correct thinking? Thanks again for the advice.

7. Aug 11, 2008

### Phrak

I'm not qualified to answer much further, but yes, you can use the inverse cube law to estimate the force at other distances once you have the force at one distance.

$$F_2\,^3 = F_1\,^3 \frac{R_1}{R_2}$$

But the center to center distances, R_1 and R_2 should be less than the greatest dimension of either your magnet or piece of metal it's attracting by a factor of 3.

The factor of 3 is a guestimate on my part. It depends on how much error you can tolerate in your data. What happens is that the force at closer distances is less than expected value using this formula. If forced to guess, you might put estimate the actual force to be 10% lower than indicated by the formula.

At closer distances it is further off. This is one reason why the break-away force is a poor indicator of the force at distance.

Baring any reponse from anyone else on this thread, you could try reposting this in the Classical Physics Folder where they might overwhelm you talking about integrating dipole moments over the volume of the magnet.

8. Aug 12, 2008

### Summit07

Okay sounds good I will begin plugging in some numbers and playing around with it. Thanks again for the advice it has helped me a ton!

9. Aug 13, 2008

### Phrak

You're welcome. I hope it helps in the real world.

10. Aug 14, 2008

### Summit07

I hope so too! ;)

I apologize in advance for this and I don't know why I didn't kick myself for this before but, I think I am going about this all wrong. Here are my thoughts. I need to figure out the force of just one magnet. After I have that, then could I plug it into the inverse square law to figure out if it could move the metal disk? Once I have that force however, what would I measure it against. Do you know of a way to measure the force needed to move an object a certain distance? In this case a 3 pound steel disk 6 feet.

Correct thinking or no?

Thank you for putting up with my questions!

11. Aug 16, 2008

### Summit07

I have been doing some more research and I've come across this equation from the website
http://www.magnetsales.com/Design/FAQs_frames/FAQs_frame.html

Here is what it says about the equation, which I have attached to this post as a jpg.

What is the governing equation for field strength relative to distance?

For a circular magnet with a radius of R and Length L, the field at the centerline of the magnet a distance X from the surface can be calculated by the following formula (where Br is the Residual Induction of the material):

Any help or advice would be greatly appreciated.

#### Attached Files:

• ###### Force Equation.JPG
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12. Aug 17, 2008

### Phrak

It looks OK. I plugged in a few values. The force drops off as a dipole should; the inverse cube of the distance. It diverges from the ideal inverse cube at small values of X as it should.

I screwed my equation, above. It should read.

$$F_2 = F_1 \left( \frac{R_1}{R_2}\right) ^3$$

13. Aug 19, 2008

### Summit07

Awesome thank you for taking a look at it for me. I think I will stick with your revised equation however. Now its just figuring out the force on one electromagnet.