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Question

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Exercise 29.47

The compound SiV3 is a type-II superconductor. At temperatures near absolute zero the two critical fields are Bc1 = 54.2 mT and Bc2 = -39.9 T . The normal phase of SiV3 has a magnetic susceptibility close to zero. A long, thin SiV3 cylinder has its axis parallel to an external magnetic field B 0 in the +x-direction. At points far from the ends of the cylinder, by symmetry, all the magnetic vectors are parallel to the x-axis. At a temperature near absolute zero the external magnetic field is slowly increased from zero.

Part A

What is the resultant magnetic field B  inside the cylinder at points far from its ends just before the magnetic flux begins to penetrate the material?

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Part B

What is the resultant magnetization M  inside the cylinder at points far from its ends just before the magnetic flux begins to penetrate the material?

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Part C

What is the resultant magnetic field B  inside the cylinder at points far from its ends just after the material becomes completely normal?

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Part D

What is the resultant magnetization M  inside the cylinder at points far from its ends just after the material becomes completely normal?

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Exercise 29.47

The compound SiV3 is a type-II superconductor. At temperatures near absolute zero the two critical fields are Bc1 = 54.2 mT and Bc2 = -39.9 T . The normal phase of SiV3 has a magnetic susceptibility close to zero. A long, thin SiV3 cylinder has its axis parallel to an external magnetic field B 0 in the +x-direction. At points far from the ends of the cylinder, by symmetry, all the magnetic vectors are parallel to the x-axis. At a temperature near absolute zero the external magnetic field is slowly increased from zero.

Part A

What is the resultant magnetic field B  inside the cylinder at points far from its ends just before the magnetic flux begins to penetrate the material?

B  =   i^T  

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Part B

What is the resultant magnetization M  inside the cylinder at points far from its ends just before the magnetic flux begins to penetrate the material?

M  =   i^A/m  

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Part C

What is the resultant magnetic field B  inside the cylinder at points far from its ends just after the material becomes completely normal?

B  =   i^T  

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Part D

What is the resultant magnetization M  inside the cylinder at points far from its ends just after the material becomes completely normal?

M  =   i^A/m  

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Explanation / Answer

a)

When Bo is just under BC1 ,the magnetic field in the material must be zero.i.e

B=0

b)

From B=Bo+uoM

=>M=-BC1/uo = -(54.2*10-3)i/(4pi*10-7)

M=-(4.31*104 A/m)i

c)

When Bo is just over BC2 ,there is zero magnetization

B=BC2=(-39.9T)i

d)

M=0

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