Magnet Contours

Magnet Contours

Jonathan Frederick, Michael Snyder, Yiting Hsieh, Chrysostomos Chrysostomou, Zach Harris

Overview • Motivation- Investigating the optical effects of a Ferrofluid Hele-Shaw Cell • Methodology- Two cameras were used to take simultaneous pictures • Conclusions to be Reached- If a Ferrofluid Hele-Shaw Cell maps contour lines?

What is a Ferrocolloidal Fluid? • “A

magnetic Ferrofluid consists of a stable colloidal dispersion of sub-domain magnetic particles in a liquid” (Rosensweig). •The magnetic subdomains are nonhomogeneous in size and shape. The optimum size for magnetic effect is approximately 5 nm.

Diagram of the Sub-domain These particles are suspended in a solvent such as water, Oleic acid, Perfluoropolyether acid, Polyphosphoric acid derivative, or Polymeric amine.

Apparatus

Procedure • MatLab programs were used to dark frame calibrate, crop, resize, drop the green and Red layers, flip, mask, and draw grid lines • MatLab was used to assemble the results into one photo per photo pair showing the front and back of the lens liquid layer. • MatLab was used to compute a cube matrix with 1/R dipole potential values and then the contour command to view different planes.

MatLab Code for Magnetic Equipotential Lines • • • • • • • • • • • • • • • • • •

%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 figure; hold on axis equal; axis([75 125 75 125 75 125]); contour(cube(:,:,70),40); hold off;

Procedure

Front and Back of Lens

Contour due to a Disc Magnet

Contour due to a Disc Magnet

Contour due to a Disc Magnet

The Problems We Arrived At • The lack of time prevented us from correlating the contour to mathematical models. • Another problem we encountered was that our references were at graduate level. • At this time, we are the only group worldwide that is attempting this research to our knowledge.

Conclusions • In strong magnetic fields, light appears to follow equipotential lines while traveling through a thin confined layer of Ferrofluid. • We believe we have taken some of the best detailed photographs of magnetic contour lines.

References • Sadiku, Matthew N.O. Elements of Electromagnetics. 3rd ed. Oxford University Press Inc. New York, NY, USA (2001). • Rosensweig, R.E. Ferrohydrodynamics. Dover Publications, Inc. Mineola, NY, USA (1997).

Questions?

• We have taken some of the most detailed pictures of the magnetic field (we’ve taken the best darn pictures ever in the history of mankind) (beat that Newton). (you too Faraday)