# Why superconductors repel magnets no matter what polarity

Gold Member
Hey everyone, got a quickie for u. I'm not sure if there is a proper answer for this question, but could ppl give me brief theories to why superconductors repel magnets no matter what polarity they are. thanx for any input!

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Chi Meson
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I'm going for brevity here. This usually takes a full class for my AP students who have already learned about electromagnetic induction. Here goes...

When a magnetic field approaches a superconductor (SC), the SC experiences a changing magnetic flux (that is, the magnetic field in a certain spot will be increasing).

A changing magnetic flux induces an emf (voltage)inside the SC that causes a charged object (an electron) to go in a circular path.

The charge that goes in a circle creates another magnetic field, and this field is always in an opposing direction to the field that created it (it repels the original magnetic field).

Since the SC has no resistance, the spinning charges do not slow down. THey keep going in circles, and therefore continue to create the magnetic field that opposes the original magnet.

Whenever the magnet changes orientation, the magnetic flux in the SC changes, and the orientation of the circles of electrons will change accordingly.

Howzat?
IF it doesn't make sense, its because I made it too simplified.

Gold Member
ok. i think i understand that, it makes sense enough for me anyway, what would be a more physics based answer to this then?? not too difficult, my brain hurts at difficult things lol

The above is the simple physics based answer. To PROVE this you got to use math.
For completness: It was postulated (can be derived as well) that in a SC the current density j is proportional to the vector potential A. So if you take the curl:

curl(j)=-1/([mu]0[lamb]L2)B (1)

this equation is called the London equation ([lamb] is the London penetration depth. Some magnetic field can penetrate the SC)
Now, from the Maxwell equations we know that

curl(B)=[mu]0j (2)

So, taking the curl on both sides of (2), then using (1) we find

[nab]2B=B/[lamb]L2 (3)

The field inside the SC has to conform to this equation. The Meissner effect now follows since (3) does not allow a uniform solution (that is B=B0). The only solution is :

B=B(0)exp(-x/[lamb]L) (4)

B(0) is the field at the edge of the SC.

Not really simple but this is the derivation of the above picture. So although it expels magnetic fields, there still is some field inside a SC

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By the way, the above rests on some assumptions. These assumtions are not necessary in a quantum theory of superconductivity. All said above follows naturally from the quantum theory. The theory is called the BCS theory of superconductivity after its inventors Bardeen, Cooper and Schrieffer.

Chi Meson