# What is the minimum area of a superconducting disk needed to flux pin against the Earth?

I'm imagining a massive ultra thin disk of YBCo or some other high temperature conductor that is surrounded by a layer of liquid nitrogen or other coolant and insulated by a layer of aerogel or other strong insulator.

If $$\Omega$$ denotes the radius of circular disk and $$\gamma$$ its thickness,

What radius and thickness would you need to be able to successfully pin such an object on Earth's magnetic field say 100 meters or so above sea level? Say at the magnetic north or south pole where the field lines are almost vertical.

Is this at all in theory possible?

## Previous Similar Questions and how they differ:

This unanswered question: Can flux pinning be used for propulsion in Earth's magnetic field?

This unanswered question of which I have posted a refinement: Quantum Locking Superconductors on Earth's Magnetic Field

This answered question: addressing the case of type I superconductors doing proper levitation, my question is different since I am interested in quantum locking with type II superconductors: superconductor levitating in earth's magnetic field?