Modeling the Magnetic Fieldof a Rectangular Ceramic Magnet

Robert KingmanOlen NettebergDouglas Show

Department of PhysicsAndrews University

Berrien Springs, Michigankingman@andrews.edu

123rd AAPT National MeetingJuly 24, 2001

Rochester, N.Y.

Outline

P Motivation

P Magnetic Field Measurements

P Magnetic Field Model of a Straight Wire

P Magnetic Field Model of a Rectangular Coil

P Magnetic Field Model of a Uniformly MagnetisedRectangular Block

P Magnetic Field Measurements of a Rectangular Coil

P Magnetic Field Measurements of a MagnetisedRectangular Ceramic Block

P Conclusion

Motivation

A need for a laboratory magnet for the following experiments:

P Standing waves on a vibrating wire

P Force on a current as a defining measurement of magnetic field

P Motional EMF experiment (The Physics Teacher, March 2001)

The new magnet

A U-shaped steel frame with a4 inch x 6 inch x 1 inch ceramicmagnet on each side.

A magnetic field of about1750 gauss in an air gapof 1.5 inches.

x

y

z

Coil sweeping through the magnetin the motional emf experiment.

Coil sweeping through two magnets with the samepolarity in the motional emf experiment

Coil sweeping through two magnets with reversedpolarity in the motional emf experiment

Force on a currentexperiment with a10-turn coil

Ceramic Magnet: 1" x 4" x 6" I = 6300 A

x

y

z

n

M

6

Magnetization surface currents of the ceramic magnet

d

The ceramic magnet behaves like a rectangular currentloop at distances large compared to the thickness d.

Surface current

Current I = M d

Magnetic moment : = I A

Magnetization field M isthe magnetic moment perunit volume

Rectangular coil 4 inch x 6 inch with 500 turnscarrying a current of 1.03 amps

Magnetic field measurements for the rectangular coil

x

y

z

z

x

yL

W

21

22

D

N

N

Bz2Bz4

Calculation of the z component ofthe coil magnetic field on the z axis

D

W/2

The z component of the coil magnetic field on the z axis

The z component of themagnetic field from sides2 and 4 on the z axis

The z component of the coil magnetic field on the x axis

The z component of the coil magnetic field on the y axis

N = 500 turnsI = 1.03 A

N = 500 turnsI = 1.03 A

Ceramic Magnet: 1" x 4" x 6" I = 6300 A

Ceramic Magnet: 1" x 4" x 6" I = 6300 A

Ceramic Magnet: 1" x 4" x 6" I = 6300 A

Thin Ceramic Magnet 0.5" x 4" x 6" I = 2700 A

Thin Ceramic Magnet 0.5" x 4" x 6" I = 2700 A

Thin Ceramic Magnet 0.5" x 4" x 6" I = 2700 A

Conclusion

P The ceramic magnet has a magnetic field characteristic ofuniform magnetization.

P The magnetic field is produced by the bound surfacecurrents of the magnetization field.

P The magnetization field in the 1 inch thick ceramic is about2.5x105 A/m.

P The surface current of the 1 inch thick ceramic is about6300 A.

P The magnetic fields of the ceramic magnets are modeledwell by an infinitesimally thin rectangular coil.

P This experiment provides an excellent application of themagnetization field for the advanced laboratory.

If you would like information about making orbuying one of these magnets contact me.

Robert KingmanDepartment of PhysicsAndrews UniversityBerrien Springs, MI 49104-0380

phone: 616-471-3431fax: 616-471-3509email: kingman@andrews.edu