Magnetic Contours

“Magnetic Contours” Author: Michael Snyder Date: May 04, 2007 Class: PHY390

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Table of Contents

Forward:

3

Summary:

3

Theory of Operation:

4

Data Processing Programs:

5

Experiential Data:

10

Conclusion:

17

References:

18

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Forward This experiment is about using a Ferrofluid Hele-Shaw Cell, that is a lens with a thin layer of sandwiched Ferrofluid to map the magnetic field contours via optic affects of light passing though the magnetic fluid. The Blue LED's of the apparatus are spaced at radially 9 degrees apart, facing inward and directed into the edge of the lens. Ferrofluid is commercially available and the common use is to cool loud speaker coils, in order to increase the power ratings of the speakers. Summary I believe this experiment was an unqualified success. There were many things than could have, and did go wrong. One of the four apparatuses completely failed the first day, but its replacement proved providential in the images it provided. This paper does not have a single mathematical equation quoted within it, so it is suggested to the reader they should bring their own. Instead, the images are compared side by side with dipole image renderings complied within MatLab. Not only do the image features from MatLab dipole models appear in the real images but many undocumented but consistent image features appear in the photographs. Rotational stress is suggested in many of the photos, equatorial jets are present in some, and vortex decay appear in others.

Drawing #1, Second Apparatus

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Theory of Operation The theory of operation of the second apparatus is that light from the forty blue LEDS ringing the teal and blue glass windows (Drawing #1) inject light between the two glass planes. Between the two glass planes is a thin layer of Ferrofluid which may or may not reflect light into the two cameras that photograph each side of the liquid simultaneously. While the true mechanism of which photons get bent 90 degrees into a camera lens and which ones do not is not understood by this paper’s author, one could come up with a scenario where this is possible. The Ferrofluid is made up of ionic magnetic molecules. In other words, each molecule has a repelling charge just like its neighbors, and each molecule has a magnetic moment. The like charges stop the molecules from clumping together into magnetic chains. The molecules are then free to bounce in every direction (Brownian motion) until they hit one of the glass planes. One could suggest that the strong external magnetic field supplied by the disc magnet used in the experiment, limited the degrees of Brownian motion experienced by the ionic molecules. Hence Brownian motion of the ionic molecules and the Lorentz Force Law all come together to trap the molecules into linear motion from one glass plane to another. Image a rubber ball bouncing between two parallel planes. Now when a photon travels between the two glass planes or maybe it is trapped by compete internal reflection and passes repeatly through the planes at a steep angle till it hits a linear moving molecule and is reflected 90 degrees into a camera lens. In other words, the Ferrofluid has molecules that are vibrating intensely. The external magnetic field traps them into a linear Z axis vibration mode, and when a photon strikes a molecule just at the right radial angle it leaves from the XY internal reflection plane onto a direct Z axis vector into a camera lens and then is captured by the camera’s CCD sensor. We bounce photons and molecules around till we get a homerun at the camera. This is all open conjecture, and is beyond the scope of this paper to pin the exact mechanism down. We know for sure, from our real world results that every so often on a nanosecond time scale, photons do leave the radial XY plane, and travel to the Z axis cameras. We also know that the probability of this happening is directly related to the external field contours passing through the Ferrofluid. The construction materials were 100mm x 6mm BK7 glass windows with a quarter wavelength flatness. PVC 4” Pipe, FerroFluid, and 5mm Deep Blue 450nm 2000mcd LED’s. The lenses were assembled by Timm Vanderelli from Ligonier, Pennsylvania. I mounted them into PVC mounts and built the edge lightning system. A DC 170volt 20ma power supply was built to power the blue LED ring. Two Nikon CoolPix E995 cameras were obtained. A dual processor computer was put together from spare parts to act as a data capture station, and it also controlled the cameras via serial cable and a free program called ‘SnapPix’. Note – Timm Vanderelli has a recently applied for nonprovisional patent on the lens construction and its optical affects.

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Data Processing Programs Trying to correlate the features in the photographs to the visual mathematical models from MatLab; here are the code snippets for both the dipole ‘cube’ matrix and the contour mapping functions. The coding practices have been kept as direct as possible. Program #1, equalpotential.m %simple code to populate a cube matrix with 1/r values for a dipole. x1=103; y1=100; z1=100; x2=97; y2=100; z2=100; for x=1:200 for y=1:200 for z=1:200 cube(x,y,z)=((x-x1)^2 + (y-y1)^2 + (z-z1)^2)^(-.5)-((x-x2)^2 + (y-y2)^2 + (z-z2)^2 )^-.5; end end end

Program #2, showme.m function h=showme(plane,lines,cube) close all; h=1; temp1=cube; temp2=cube; temp3=cube; figure; hold on axis equal; axis([75 125 75 125 75 125]); contour(temp1(:,:,plane),lines); hold off; figure; hold on axis equal; axis([75 125 75 125 75 125]); temp2(:,:,plane)=temp2(plane,:,:); contour(temp2(:,:,plane),lines); hold off; figure; hold on axis equal; axis([75 125 75 125 75 125]); temp3(:,:,plane)=temp3(:,plane,:); contour(temp3(:,:,plane),lines); hold off;

These two programs create a cube matrix and then plots contours of the matrix into three figures, one for each plane.

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Program #3, makedark.m I(1,:,:,:)=imread('dscn3927.tif'); I(2,:,:,:)=imread('dscn3928.tif'); I(3,:,:,:)=imread('dscn3929.tif'); I(4,:,:,:)=imread('dscn3986.tif'); I(5,:,:,:)=imread('dscn3987.tif'); I(6,:,:,:)=imread('dscn3925.tif'); I(7,:,:,:)=imread('dscn3926.tif'); I(8,:,:,:)=imread('dscn3990.tif'); I(9,:,:,:)=imread('dscn3989.tif'); I(10,:,:,:)=imread('dscn3988.tif'); dframe=zeros(1536,2048,3); for i=1:1536 for j=1:2048 for k=1:3 dframe(i,j,k)=mean(I(:,i,j,k)); end end end

The ‘makedark.m’ program performs median processing of ten dark frame photographs in order to average out the noise from each photo run. The ‘subtrackdark.m’ program then advances through the photos (from the runs) and subtracts the created dark frame. This is the only calibration that was used, and it proved surprisingly effective. The program then increases the contrast by a factor of five, after removing the noise. Program #4, subtractdark.m rootname = 'dscn'; extension = '.tif'; savename = 'laserone'; for i=4192:4205 rfilename = [rootname, int2str(i), extension] sfilename = [savename, int2str(i), extension] m=double(imread(rfilename)); m(:,:,3)=[]; m(:,:,1)=[]; imwrite(uint8(round(5*(m-dframe))),sfilename); end

The final step is the ‘masterprocess.m’ program then takes the contrast increased, noise reduced photos, and processes batches paired front/back photos into side by side photos. It crops the photos to the same size, enlarges one to match the two photo matrixes, and then flips it so both appear to be from the same side. This is done so the viewer can see the front and back contour images at the same time. The reason I included the programs is so the reader fully understands that finished photos have not been changed in any subtle way. All the programs use a sledgehammer approach to calibrate, crop, resize, drop the green and red dimensions, flip, mask, draw grid lines, and then assemble the results into one photo per pair produced during the experimental runs.

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Program #5.1, masterprocess.m I01=double(imread('runtwo4024.tif')); I03=double(imread('runtwo4028.tif')); I05=double(imread('runtwo4029.tif')); I07=double(imread('runtwo4032.tif')); I09=double(imread('runtwo4050.tif')); I11=double(imread('runtwo4051.tif')); I02=double(imread('runtwo5171.tif')); I04=double(imread('runtwo5175.tif')); I06=double(imread('runtwo5176.tif')); I08=double(imread('runtwo5179.tif')); I10=double(imread('runtwo5197.tif')); I12=double(imread('runtwo5198.tif')); I01(:,:,1)=[]; I03(:,:,1)=[]; I05(:,:,1)=[]; I07(:,:,1)=[]; I09(:,:,1)=[]; I11(:,:,1)=[]; I02(:,:,1)=[]; I04(:,:,1)=[]; I06(:,:,1)=[]; I08(:,:,1)=[]; I10(:,:,1)=[]; I12(:,:,1)=[]; I01(:,:,1)=[]; I03(:,:,1)=[]; I05(:,:,1)=[]; I07(:,:,1)=[]; I09(:,:,1)=[]; I11(:,:,1)=[]; I02(:,:,1)=[]; I04(:,:,1)=[]; I06(:,:,1)=[]; I08(:,:,1)=[]; I10(:,:,1)=[]; I12(:,:,1)=[]; C01=I01(250:1536,442:1728); C03=I03(250:1536,442:1728); C05=I05(250:1536,442:1728); C07=I07(250:1536,442:1728); C09=I09(250:1536,442:1728); C11=I11(250:1536,442:1728); C02=I02(78:1528,540:1990); C04=I04(78:1528,540:1990); C06=I06(78:1528,540:1990); C08=I08(78:1528,540:1990); C10=I10(78:1528,540:1990); C12=I12(78:1528,540:1990);

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Program #5.2, masterprocess.m C01=imresize(C01,[1451 1451],'bicubic'); C03=imresize(C03,[1451 1451],'bicubic'); C05=imresize(C05,[1451 1451],'bicubic'); C07=imresize(C07,[1451 1451],'bicubic'); C09=imresize(C09,[1451 1451],'bicubic'); C11=imresize(C11,[1451 1451],'bicubic'); C02=flipud(C02); C04=flipud(C04); C06=flipud(C06); C08=flipud(C08); C10=flipud(C10); C12=flipud(C12); C02=fliplr(flipud(C02')); C04=fliplr(flipud(C04')); C06=fliplr(flipud(C06')); C08=fliplr(flipud(C08')); C10=fliplr(flipud(C10')); C12=fliplr(flipud(C12')); C01=fliplr(flipud(C01')); C03=fliplr(flipud(C03')); C05=fliplr(flipud(C05')); C07=fliplr(flipud(C07')); C09=fliplr(flipud(C09')); C11=fliplr(flipud(C11')); M02=uint8(255*(C02<21)); M04=uint8(255*(C04<21)); M06=uint8(255*(C06<21)); M08=uint8(255*(C08<21)); M10=uint8(255*(C10<21)); M12=uint8(255*(C12<21)); M01=uint8(255*(C01<21)); M03=uint8(255*(C03<21)); M05=uint8(255*(C05<21)); M07=uint8(255*(C07<21)); M09=uint8(255*(C09<21)); M11=uint8(255*(C11<21)); P01=hmf(M01); P02=hmf(M02); P03=hmf(M03); P04=hmf(M04); P05=hmf(M05); P06=hmf(M06); P07=hmf(M07); P08=hmf(M08); P09=hmf(M09); P10=hmf(M10); P11=hmf(M11); P12=hmf(M12);

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Program #5.3, masterprocess.m for i=26:100:1451 P01(:,i)=255; P01(i,:)=255; P02(:,i)=255; P02(i,:)=255; P03(:,i)=255; P03(i,:)=255; P04(:,i)=255; P04(i,:)=255; P05(:,i)=255; P05(i,:)=255; P06(:,i)=255; P06(i,:)=255; P07(:,i)=255; P07(i,:)=255; P08(:,i)=255; P08(i,:)=255; P09(:,i)=255; P09(i,:)=255; P10(:,i)=255; P10(i,:)=255; P11(:,i)=255; P11(i,:)=255; P12(:,i)=255; P12(i,:)=255; end F01=([C01,C02;imadd(uint8(C01),P01),imadd(uint8(C02),P02)]); F02=([C03,C04;imadd(uint8(C03),P03),imadd(uint8(C04),P04)]); F03=([C05,C06;imadd(uint8(C05),P05),imadd(uint8(C06),P06)]); F04=([C07,C08;imadd(uint8(C07),P07),imadd(uint8(C08),P08)]); F05=([C09,C10;imadd(uint8(C09),P09),imadd(uint8(C10),P10)]); F06=([C11,C12;imadd(uint8(C11),P11),imadd(uint8(C12),P12)]); imwrite(F01,'p01.tif'); imwrite(F02,'p02.tif'); imwrite(F03,'p03.tif'); imwrite(F04,'p04.tif'); imwrite(F05,'p05.tif'); imwrite(F06,'p06.tif'); imwrite(F01,'p01.jpg','jpg','quality',80); imwrite(F02,'p02.jpg','jpg','quality',80); imwrite(F03,'p03.jpg','jpg','quality',80); imwrite(F04,'p04.jpg','jpg','quality',80); imwrite(F05,'p05.jpg','jpg','quality',80); imwrite(F06,'p06.jpg','jpg','quality',80);

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Experiential Data

Photograph #P23, Clearly the Best of the Series.

This photo is simply the best. It was taken during the second photo run by group member Yiting Hsieh. The ring magnet was suspended on a chopstick and held up to the center of the lens apparatus. The specifications of the magnet are NdFeB Br Max 12,700 Gauss, 1 1/2" x 1/2" x 3/8". It was purchased from wondermagnet.com.

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The poles are on the flat ends of the disc magnet. When you zoom in on the picture, one would see there are no ‘B’ field lines connecting the flat faces to each other. Instead there is a hyperbola shape running orthogonal to the expected magnetic ‘B’ field. These are in fact, the equipotential contour lines anyone would expect from a charged dipole or a magnetic contour. One problem being while we have a charged ions within the solution; it is clearly the 1.2 Tesla magnet is producing the visual affect. Magnetostatics do not have an ‘E’ field! Even if it did, how would one get an equipotential line to be photographed? This is like taking the first satellite photograph of earth, seeing the Longitude and Latitude lines on the photograph, and comparing it to land based maps and thinking all is well. One small problem, Longitude, Latitude, and Equipotential lines are mathematical identities! It is nearly unexplainable; unless one considers the possibility that the light may be following the variable geodesics of the dipole spherical surfaces, as it was bisected by the Cartesian plane of the Ferrofluid Hele-Shaw Cell. “Geodesics preserve a direction on a surface (Tietze 1965, pp. 26-27) and have many other interesting properties. The normal vector to any point of a geodesic arc lies along the normal to a surface at that point (Weinstock 1974, p. 65).” (mathworld.wolfram.com) Compare Photograph P23 to Dipole Rendering #1. The units are arbitrary but I rotated it a few degrees so one could match up the orientation. The lines seem to match perfectly.

125 120 115 110 105 100 95 90 85 80 75

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Dipole Rendering #1

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Photograph #P14, Cropped to Show the ‘Michael’s Tree’ Pattern. When I saw this pattern on quite a few of the photos, I named it ‘Michael’s Tree’. During the experiment we had trouble positioning the magnets. One easy solution was just to set it on edge, resting with one edge on the PVC and one edge pressing against the glass. This seems to distort the hyperbola but it is still clearly identifiable. Notice the equatorial jet on the left hand same side image.

125 120 115 110 105 100 95 90

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Dipole Rendering #2 - 12 -

The specifications of the magnet are NdFeB Br Max 12,100 Gauss, 1 1/4" x 1/2". The poles are on the flat sides. This is the same magnet that shows up in pictures P01-P18. Speaking of equatorial jets, now things go from merely strange, straight to the far out reaches of J.C. Maxwell vortex rotation. To quote Maxwell from page 169 of his March 1861 publication in Philosophical Magazine. Third paragraph down. “The vortices, according to hypothesis, will be in the direction shown by the arrows in fig.3, that is, in a plane perpendicular to the lines of force, and revolving in the direction of the hands of a watch when observed from ‘s’ looking towards ‘n’.

Bitmap Image #1, Section of Maxwell’s 1861 Publication. It is easy to realize a plane perpendicular to the lines of force is a dipole contour map. Thinking maybe we didn’t photograph anything new, but instead something that is 246 years old predicted by Maxwell. Does a Maxwell Vortex equal a Geodesic? Unfortunely, we didn’t think it was important to record which poles were facing which way. Yet, I will show you a few photos selected from many photos that strongly remind one of a single large vortex rotation lined up with the poles. In these following photos, the magnets have their poles directly pressed against the glass. Both cameras are about 21cm away from the centered liquid layer. The magnet is 6mm away from the liquid. Holding an object against a plane of glass and looking directly at the object at the same elevation should produce a viewed object about the same original size. Snell’s law should not affect the viewed image size at the same elevation on the same axis. Yet, in our photos, the opposite side clearly showed the magnet was obscured by something. Only a smaller portion of the magnet is clearly visible, reminding me of an event horizon. In other words, the opposite side pictures always seem to show a smaller magnet diameter at the same elevation. We had used both sides of the lens assembly for the various magnet positions, so it is not one camera or the other camera is systematically showing a scaled magnet size error, because both cameras had similar pictures.. - 13 -

My group measured the data for magnet size, outside diameter of the same side image and opposite side inside diameter. In other words, there are three rings in each direct pole photo set. On the same side there is a larger halo light ring, then the seen and measured magnet diameter, and then always a smaller diameter on the other side.

Photograph #P03, Cropped to Show Three Different Rings.

Photograph #P15, Cropped to Show Three Different Rings.

The little magnet in the pictures is 1/4"x1/2” 12,700 Gauss used to hold the larger magnet in place for the pictures. Notice the left hand diameter image of the larger magnet doesn’t match the right side image of the larger magnet. All the pole pictures have this behavior.

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Table #1, Measured Sizes of Viewed Magnet Diameters Magnet Diameter Size(Pixels) 243 240 239 240 245 243 238

Inside Diameter (Pixels) 138 137 140 158 131 147 145

Outside Diameter (Pixels) 326 324 340 323 335 375 326

Mean

240

140

326

Standard Dev

2.54

8.71

18.48

±1.89

±6.45

±13.69

Photo P03 P15 P16 P04 P05 P08 P12

Confidence@95%

Directly viewing the top of a dipole should look something like this: 125 120 115 110 105 100 95 90 85 80 75

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Dipole Rendering #3 I’m going to make the claim that the reason we didn’t get a dipole picture from the top (pole facing) is that Maxwell’s darn vortex got in the way! Imagine the larger halo ring is the base of the vortex moving around the magnet. The smaller ring is then viewed as the vortex termination point passing into the magnet. The outside diameter is the hurricane and the inside diameter is the eye.

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Think of a common bathtub drain. At full speed the water vortex allows you the see the shining chrome drain grid at the bottom, but what you see is a smaller subset of the true drain size. Notice the many vortexes of the grid drain join together into one large one. I’m saying the full size magnet pole is the drain size, and we are seeing less of it on the opposite side because the side of Maxwell’s vortex is obscuring it.

Photograph #P03, Cropped to Show the Tangential Lines.

Finally take a good look at the tangential lines on the left hand side (opposite side image). Notice they seem problematic because they are not directly following the contours like they should in Dipole Rendering #3. The contour lines illuminated by the nearby LEDS (every 9 degrees) are not the circles they should be, but instead they are ellipses. Consider this; if they are following the contours of a moving vortex terminating directly into the pole face, then maybe that is the right behavior. They are falling into the magnet while circling it. Then the lines join into a uniform circle, similar to an event boundary. There are many pictures of tangential lines in the data sets. To me, they seem to be slightly off dead center where they intersect over the magnet. Thinking this seems consistent with Maxwell’s Theory. The photographed tangential lines are ‘falling’ into the center of the magnet. The ones originating from the right side seem to be falling a little faster than the ones originating from the left hand side. Yet, if you compare them to the idealized Dipole Rendering #3; I think they are still recognizable as contour lines. Prograde and retrograde tangential contour/geodesic lines.

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Conclusion The conclusion is that at very least, the reader should be asking oneself how do you take a picture of Longitude, Latitude, or Equipotential line? Why would a liquid magnet form a contour line? At the most, maybe the reader should start wondering about just maybe Professor Maxwell was correct in is 1861 paper about Magnetic Vortexes. We do use his equations on a daily basis. I claim my measurements group has taken the most detailed pictures of magnetic contour lines that have ever been viewed in human history. The hyperbola seen in picture P23 speaks for itself. It is as beautiful as it is unexplainable, unless one considers that the light is following the geodesics of spherical surfaces centered at the dipole poles, and bisected by the plane of the Ferrofluid Hele-Shaw Cell. The datasets are publicly available, I would encourage readers to download them and reach their own conclusions. My undergrad experiment continues next semester and I will post my results in a timely manner.

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References

Maxwell, J.C. "Philosophical Magazine." On Physical Lines of Force. Part 1. March 1861: 161-175. Tourinho, F. A. Static magneto optical birefringence of new Electric Double Layered Magnetic Fluids. (Online) Available http://www.scielo.br/scielo.php?pid=S010397332001000300008&script=sci_arttext 9 May 2007. The Flux Resonator. (Online) Available http://www.magnetostatics.us/index.htm 4 May 2007. Mechanical Universe and Beyond #36. Videocassette. Time Index 17:00. California Institute of Technology and Intelecom., 1985 Rowland, Todd. Geodesic. (Online) Available http://mathworld.wolfram.com/Geodesic.html 9 May 2007.

Download the Complete P01-P24 Data Set at: http://www.esnips.com/doc/3a743282-6ae4-4ef0-9278-0e6d0527c690/Zip-File-With-All-of-the-JpgPictures or http://www.esnips.com/web/measurements All Rights Reserved, M. Snyder May 04/2007

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