Question

5. The superconductor is characterized by the infinite conductivity and zero magnetic field inside it. The latter property of "magnetic flux exclusion" is known as the Meissner effect. The magnetic dipole, $\vec{\mu} = m \cdot \vec{e}_z$, constrained to point in the z direction levitates above the infinite superconducting plane which is placed at z = 0. (a) Find the height h at which the dipole "floats" above the superconductor in the gravitational field $-g \cdot \vec{e}_z$, if the mass of the dipole is M. Hint: recall method of images and formulate appropriate boundary conditions on the surface of the superconductor. (b) Compute surface current $\vec{K}(r, \varphi, z = 0)$ in the superconductor. (c) [Extra Credit] If the dipole $\vec{\mu}$ is free to rotate, what orientation will it adopt, and how high above the surface of the superconductor will it float?

          5. The superconductor is characterized by the infinite conductivity and zero magnetic field
inside it. The latter property of "magnetic flux exclusion" is known as the Meissner
effect. The magnetic dipole, $\vec{\mu} = m \cdot \vec{e}_z$, constrained to point in the z direction levitates
above the infinite superconducting plane which is placed at z = 0.
(a) Find the height h at which the dipole "floats" above the superconductor in the
gravitational field $-g \cdot \vec{e}_z$, if the mass of the dipole is M. Hint: recall method
of images and formulate appropriate boundary conditions on the surface of the
superconductor.
(b) Compute surface current $\vec{K}(r, \varphi, z = 0)$ in the superconductor.
(c) [Extra Credit] If the dipole $\vec{\mu}$ is free to rotate, what orientation will it adopt,
and how high above the surface of the superconductor will it float?

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5 the superconductor is characterized by the infinite conductivity and zero magnetic field inside it the latter property of magnetic flux exclusion is known as the meissner effect the magnet 55828

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University Physics with Modern Physics

Hugh D. Young 14th Edition

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Solved by Expert Khoobchandra Agrawal

09/11/2020

Step 1

The magnetic dipole moment is given by $\vec{\mu} = m \vec{e}_z$. Since the superconductor excludes magnetic flux, we can use the method of images. The image dipole will have a dipole moment $\vec{\mu}' = -m \vec{e}_z$ located at $z = -h$. Show more…

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5. The superconductor is characterized by the infinite conductivity and zero magnetic field inside it. The latter property of "magnetic flux exclusion" is known as the Meissner effect. The magnetic dipole, $\vec{\mu} = m \cdot \vec{e}_z$, constrained to point in the z direction levitates above the infinite superconducting plane which is placed at z = 0. (a) Find the height h at which the dipole "floats" above the superconductor in the gravitational field $-g \cdot \vec{e}_z$, if the mass of the dipole is M. Hint: recall method of images and formulate appropriate boundary conditions on the surface of the superconductor. (b) Compute surface current $\vec{K}(r, \varphi, z = 0)$ in the superconductor. (c) [Extra Credit] If the dipole $\vec{\mu}$ is free to rotate, what orientation will it adopt, and how high above the surface of the superconductor will it float?

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Transcript

00:03 Hello everyone this is the review problem based on masoner's effect.

00:10 So you know about it, it happens only in case of superconductor inside the superconductor magnetic field is zero.

00:18 So this problem is based on this.

00:20 Now here it is given a vertical solenoid with length 120 cm that is 1 .2 meter and diameter 2 .5 centimeters and diameter 2 .5 centimeter that is 0 to 5 meter consists of 1400 turns and carries the counterclockwise current of 2 ampere find the magnetic field in vacuum inside the coil so magnetic field inside the coil we have to find b part find the energy density of the magnetic field energy density we have to find c now superconducting wire is inserted part way into the solenoid, its upper end is far outside the solenoid where the magnetic field is negligible.

01:46 The lower end of the bar is deep inside the solenoid.

01:50 Identify if you draw the diagram, diagram will be like this.

01:56 This is the solenoid.

02:03 So i am drawing the diagram for three parts.

02:10 This is the magnetic field lines of solenoid.

02:16 Here, this is the bar magnet made of superconductor.

02:49 A diameter of the bar is given 2 .2 cm.

03:11 In c part we required the direction of current so that net magnetic field is to be 0.

03:23 The field of the cylinder ad accepts the force on the current in superconductor.

03:29 Identify the force...

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