# Magnetic field at a distance - epxression

1. Aug 30, 2007

### rsr_life

Hello,

I have a cylindrical Neodymium permanent magnet. I need to find the pull force of the magnet at various distances from the magnet. Is there an expression relating the pull force(or attractive force) to the magnetic flux density B and the distance from the cylindrical magnet? What is the expression that tells us how the B varies with distance?

The parameters I have for the magnet are here

http://www.kjmagnetics.com/proddetail.asp?prod=D2C .

Thanks,

rsr_life

2. Aug 30, 2007

### Staff: Mentor

3. Aug 30, 2007

### rsr_life

The wiki doesn't seem to have an expression listed for calculating magnetic flux density at a distance for a cylindrical permanent magnet. There's no current involved, so I just want to be able to simulate and get field values at different points from the magnet.

Seems there should be a straightforward expression to do this, maybe involving partial derivatives.

Thanks.

4. Aug 31, 2007

### mdelisio

Far enough away, most magnets can be approximated as a magnetic dipole moment m, which is a vector. For a magnetic dipole m at the origin and oriented in the z-direction, you get

$$\vec{B} = {\mu_o m \over {4\pi r^3}} (2\cos\theta \hat{r} + \sin\theta\hat{\theta})$$

The trick for your problem will be to find out a good guess at m. As usual, Wikipedia has some good information.

5. Aug 31, 2007

### rsr_life

Thanks for that. What about points closer to the magnet - near the surface, for example, where the gradient is steeper?

6. Aug 31, 2007

### dlgoff

Maybe you can find an equation by experiment. Could you use some type of spring device (to messure weight) with a iron-mass on it and find the force at different points around the magnet? Say; leave the spring hanging and moving the magnet at different positions under the mass?