Magnetic Forces

Radial forces

The forces between a coil and some ferromagnetic material is highly depending on the distance from the magnet. An approximation of the stray field (for large r)

B = Bo * r ^ (-3)

and the field gradient is

dB/dr = - 3 Bo * r ^ (-4)

The force is proportional to the product of the induced field in the ferromagnet and the field gradient. The induced field is proportional to the stray field, for low fields, but gets constant when the ferromagnet saturates. Therefore the force between the coil and a ferromagnetic piece is proportional to the power of -4 of the distance in high fields

F ~ r ^ (-4)

and proportional to the power of -7 of the distance in low fields.

When the distance is kept constant, the relation between the force and the central field is quadratic for low fields, and gets linear for higher fields.

Taking the torque into account

In general, the forces or not only radial but also tangential, inducing a torque onto the magnet. For estimating the forces on the fixation, we need to take into account the distance of the fixation points from the coil center.

For MA7, with a mean coil radius of about 100 m and fixation points at about 150 mm from the coil center, we get the following:

Ro: object distance (mm)
phi: angle (deg) between field direction and direction of object, for maximum force on fixation
Fp: force when object on magnet axis (in field direction) Ft: maximum total force on fixation

Approximation of Forces (taken from OI Magnet Manual)

As a rough guideline the following estimation can be made. For iron placed in a gradient of 500 G/m the force due to the field is equal to the mass of the object. For larger field gradients: Force = 10 * mass * gradB / 500 with Force, mass and gradB in (N, kg, Gauss/m).

typical Field Limits for Common Devices

The following devices should be kept outside these limits:

Fields larger than stated below might affect the following devices: