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Ferromagnetic particle force

A small ferromagnetic particle is placed next to the circular current currying loop of wire.

Problem type:
Axisymmetric problem of DC magnetics

Geometry:

Ferromagnetic particle force

Particle diameter 1 mm.

Given:
I = 50 A - current in the wire;
μ = 1000 - relative magnetic permeability of the particle.

Task:
Calculate the force acting on the particle placed at the axis of the ring as a function of the distance from the ring center.

Solution:
Flux density distribution produced by the circular current could be calculated analytically. However the particle causes local field distortion. Since the particle and ring feature cylindrical symmetry the model simulated as 2D axisymmetric. Axis of rotation is horizontal.

Results:
Flux density B(z) peak value is 0.78 mT (located at the ring center)
Flux density gradient dB(z)/dz peak value is 17 mT/m (located 2 cm away from the ring center)

Flux density B(z) and gradient dB(z)/dz distribution along the ring axis:

Loop ring current flux density gradient

Magnetic field distortion caused by the ferromagnetic particle.

Magnetic flux distortion cased be magnetic particle

Force acting on a particle as a function of distance from the ring center:

Distance, z

Force, Fz

2.5 cm

0.97·10-8 N

2 cm

1.2·10-8 N

1.5 cm

1.3·10-8 N

1 cm

1.2·10-8 N

0.5 cm

0.75·10-9 N

LabelMover tool is used to automate the force vs. distance dependency calculation.
Magnetic force is maximal at 1.5 cm away from the ring center.

Force acting on a particle as a function of distance from the ring center

Download icon Download simulation files (files may be viewed using any QuickField Edition).

There are no restrictions applied to the QuickField Student Edition postprocessors.
You can view field maps, make plots, calculate integrals and print pictures in the same way that the Professional Edition users do.