Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1...
Transcript of Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1...
![Page 1: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/1.jpg)
Modeling the Magnetic Fieldof a Rectangular Ceramic Magnet
Robert KingmanOlen NettebergDouglas Show
Department of PhysicsAndrews University
Berrien Springs, [email protected]
123rd AAPT National MeetingJuly 24, 2001
Rochester, N.Y.
![Page 2: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/2.jpg)
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
![Page 3: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/3.jpg)
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)
![Page 4: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/4.jpg)
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
![Page 5: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/5.jpg)
![Page 6: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/6.jpg)
![Page 7: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/7.jpg)
![Page 8: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/8.jpg)
Coil sweeping through the magnetin the motional emf experiment.
![Page 9: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/9.jpg)
![Page 10: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/10.jpg)
Coil sweeping through two magnets with the samepolarity in the motional emf experiment
![Page 11: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/11.jpg)
![Page 12: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/12.jpg)
Coil sweeping through two magnets with reversedpolarity in the motional emf experiment
![Page 13: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/13.jpg)
![Page 14: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/14.jpg)
Force on a currentexperiment with a10-turn coil
![Page 15: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/15.jpg)
![Page 16: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/16.jpg)
Ceramic Magnet: 1" x 4" x 6" I = 6300 A
x
y
z
![Page 17: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/17.jpg)
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
![Page 18: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/18.jpg)
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
![Page 19: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/19.jpg)
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
![Page 20: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/20.jpg)
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
![Page 21: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/21.jpg)
The z component of the coil magnetic field on the x axis
![Page 22: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/22.jpg)
The z component of the coil magnetic field on the y axis
![Page 23: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/23.jpg)
N = 500 turnsI = 1.03 A
![Page 24: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/24.jpg)
N = 500 turnsI = 1.03 A
![Page 25: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/25.jpg)
Ceramic Magnet: 1" x 4" x 6" I = 6300 A
![Page 26: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/26.jpg)
Ceramic Magnet: 1" x 4" x 6" I = 6300 A
![Page 27: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/27.jpg)
Ceramic Magnet: 1" x 4" x 6" I = 6300 A
![Page 28: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/28.jpg)
Thin Ceramic Magnet 0.5" x 4" x 6" I = 2700 A
![Page 29: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/29.jpg)
Thin Ceramic Magnet 0.5" x 4" x 6" I = 2700 A
![Page 30: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/30.jpg)
Thin Ceramic Magnet 0.5" x 4" x 6" I = 2700 A
![Page 31: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/31.jpg)
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.
![Page 32: Modeling the Magnetic Field of a Rectangular Ceramic Magnet · P The magnetization field in the 1 inch thick ceramic is about 2.5x10 5 A/m. P The surface current of the 1 inch thick](https://reader035.fdocuments.us/reader035/viewer/2022070913/5fb490a7b0b78c518816b329/html5/thumbnails/32.jpg)
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: [email protected]