## Meissner Effect

Walter Meissner and Robert Ochsenfeld discovered a magnetic phenomenon in 1933. He studied that superconductors are not just perfect conductors and give the Meissner effect.

*When a weak magnetic is applied to a superconducting specimen at a temperature below transition temperature T _{c} the magnetic flux lines are expelled. This phenomenon is the Meissner effect.*

Thus according to Meissner, when superconductors cooled below its transition temperature. Under the effect of magnetic field, the lines of induction B pushed out. The Meissner effect finds that a bulk superconductor behaves as if B = 0 inside the specimen.

**Effect of Magnetic Field**

Suppose that both the ideal conductor and superconductor are above their critical temperature. And they both have electrical resistance and are in a normally conducting state. When magnetic field applied. As a result of this, the field penetrates in both the materials. After that both samples are then cooled so that the ideal conductor now has zero resistance. It is found that the ideal conductor maintains a magnetic field in its interior. Whereas a superconductor expels the magnetic field from inside it.

**Diamagnetism is an essential property for Superconductor**

The Meissner effect suggests that perfect diamagnetism is an essential property of the superconducting state. Hence, We can see this in the following calculation as well.

Let us try to find out mathematically. Under normal condition the magnetic induction inside the specimen is

B = μ_{0}(H+I)

Where I is the magnetization produced inside the specimen and H is simply the external applied magnetic field.

According to the Meissner effect, When the specimen is in superconducting state, B is zero i.e. B=0.

B = μ_{0}(H+I)

0 = μ_{0}(H+I)

H= -I

χ = H/I =-1

Thus the material acts as a perfectly diamagnetic because for diamagnetic material susceptibility χ = -1.

**Contradiction** to Meissner Effect

From the characterization of a superconductor as a medium of zero resistivity result B = 0 cannot be derived . Let us consider a superconducting material in a normal state. From ohm’s law, the electric field

E=Jρ

On cooling the material to its transition temperature resistivity becomes zero this implies ρ tends to zero. If J has finite value, E must be zero.

From Maxwell’s equations

∇ × E = – dB/dt

Under superconducting condition

Since E is zero. So the right hand side of the equation is also zero.

dB/dt =0

or B=constant.

This means that on cooling the specimen to the transition temperature, the magnetic flux passing through the specimen should not change. Thus the Meissner effect contradicts the result.

London equation give the theoretical base to the Meissener effect. It observes that the magnetic field inside the specimen decay over a 20-40nm distance. We can observe this in terms of London penetration depth.

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