The diamagnetic sphere is subjected to the following forces: Gravitation, Archimedean upward thrust and field gradient force created by the two magnets.

The paramgnetic solution has the role to neutralizeg the

gravitational forces, permitting the sphere

to levitate upwards with the help of the field gradient between

the two magnets.

Thank you for your response. Do you mean to say paramagnetic solution's density is providing a buoyant force (archimedean thrust) counteracting the gravitational forces? I understand that having the sphere being close to neutrally buoyant helps tremendously for levitation.

To clarify my question, see the attached png. The equations is the result of a force balance between gravity+buoyancy (1st term) and magnetic field forces (2nd term). Your answer pertains to the first term in the equation, while I was asking for a description related to the magnetic susceptibility in the second term.

• Levitation of the diamagnetic sphere is governed by the condition (Rhog-Rhom)g+ (khig-khim)/2mu0 grad2(B)=0
• Thus, the presence of a paramagnetic solution (as Gd.MnCl2 or Dy.(NO3)3,... ) would change the apparent susceptibility Khiapp=(khig-khim) and density:Rhoapp = (Rhog-Rhom) leading to enhance the force exerced on the sphere.
• The force created by the paramagnetic solution is called "magnetic archimedean thrust". With this procedure, the levitation could be reinforced by several orders of magnitude (up to 6 !!).
• The shape of the diamagnetic body is important :with the spherical form, the demagnetization effects are minimized
• Filed gradinet is equally important to enhance the levitation effect

erratum

sorry,

DRho g+ Dkhi/2mu0 grad(B2)=0

DRho=(Rhog-Rhom)

Dkhi=(khig-khim)

Hi Mohamed, would you say the force created by the media is caused by the media trying to be closer to the magnets?

It's Archimedes' Principle applied in a magnetic field. The paramagnetic fluid is attracted more strongly than the diamagnetic object, which isn't even attracted at all, hence it adds to the upthrust.

Interestingly, in Maxwell's 1861 paper (http://vacuum-physics.com/Maxwell/maxwell_oplf.pdf ) the whole issue of diamagnetism versus paramagnetism is explained in a manner as like Archimedes' Principle in his sea of molecular vortices. Read from page 170 (page 10 in the pdf file in the above link) beginning at the third paragraph were he says "We now proceed to examine the second term - - - - " and read on into page 171.

Thanks Frederick, that should be able to help me get my head around things better.