Magnetic Properties of Materials

A magnetic dipole is under the influence of two magnetic fields. The angle between the field direction is $60°$and one of the fields has a magnitude of $1.2\times {10}^{-2} \mathrm{T}$. If the dipole comes to stable equilibrium at an angle of $15°$with this field . What is the magnitude of the other field?

A monoenergetic $\left(18 \mathrm{keV}\right)$ electron beam initially in the horizontal direction is subjected to a horizontal magnetic magnetic field of $0.04 \mathrm{G}$ normal to the initial direction. Estimate the up or down deflection of the beam over a distance of $30 \mathrm{cm}, {\mathrm{m}}_{\mathrm{e}}=9.11\times {10}^{-31} \mathrm{kg}$ [NOTE: Data in this exercise are so chosen that the answer will give you an idea of the effect of Earth's magnetic field on the motion of an electron from an electron gun to the screen on a TV set]

A sample of paramagnetic salt contains $2.0\times {10}^{24}$ atomic dipoles each of dipole moment $1·5\times {10}^{-23}$${\mathrm{JT}}^{-1}$. The sample is placed under a homogeneous magnetic field of $0.64 \mathrm{T}$ and cooled to a temperature of  $4.2 \mathrm{K}$. The degree of magnetic saturation achieved is equal to $15$ percent. What is the total dipole moment of the sample for a magnetic field of $0.98 \mathrm{T}$ and a temperature of  $2.8 \mathrm{K}$? (Assume Curie's Law).

A Rowland ring of mean radius $15 \mathrm{cm}$ has $3500$ turns of wire wound on a ferromagnetic core of relative permeability $800$. What is the magnetic field $\mathrm{B}$ in the core for a magnetising current of $1.2 \mathrm{A}$?

The magnetic moment vectors ${\mathrm{\mu }}_{\mathrm{s} }$and ${\mathrm{\mu }}_{\mathrm{l}}$ associated with the intrinsic spin angular momentum $\mathrm{S}$ and orbital angular momentum $\mathrm{L}$ respectively of an electron are predicted by Quantum theory (and verified experientially to a high accuracy) to be given by:

$$\begin{gathered} {\mathrm{\mu }}_{\mathrm{s}}=-\left(\frac{\mathrm{e}}{\mathrm{m}}\right)\mathrm{S} \\ {\mathrm{\mu }}_{\mathrm{l}}=-\left(\frac{\mathrm{e}}{2\mathrm{m}}\right)\mathrm{L} \end{gathered}$$

Which of these relations is in accordance with the results expected classically? Outline the derivation of classical result.

A long straight horizontal cable carries a current of $2.5 \mathrm{A}$ in the direction ${10}^{°}$ south of west to ${10}^{°}$ north of east. The magnetic meridian of the place happens to be ${10}^{°}$west of the geographic meridian. The earth's magnetic field at the location is $0.33 \mathrm{G}$, and the angle of dip is zero. Locate the line of neutral points (ignore the thickness of the cable)? (At neutral points, magnetic field due to a current - carrying cable is equal and opposite to the horizontal component of earth's magnetic field.) 

A certain region of space is to be shielded from magnetic fields. Suggest a method.

What kind of ferromagnetic material is used for coating magnetic tapes in a cassette player, or for building 'memory stores' in a modern computer?

Answer the following question.

'A system displaying a hysteresis loop such as a ferromagnet, is a device for storing memory?' Explain the meaning of this statement.

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The hysteresis loop of a soft iron piece has a much smaller area than that of a carbon steel piece. If the material is to go through repeated cycles of magnetisation, which piece will dissipate greater heat energy?

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Explain qualitatively on the basis of domain picture the irreversibility in the magnetization curve of a ferromagnet.

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Would the maximum possible magnetization of a paramagnetic sample be of the same order of magnitude as the magnetization of a ferromagnet?

Answer the following question:

Magnetic field lines are always nearly normal to the surface of a ferromagnet at every point. (This fact is analogous to the static electric field lines being normal to the surface of a conductor at every point.) Why?

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Is the permeability of a ferromagnetic material independent of the magnetic field? If not, is it more for lower or higher fields?

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If a toroid uses bismuth for its core, will the field in the core be (slightly) greater or (slightly) less than when the core is empty?

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Why is diamagnetism, in contrast, almost independent of temperature?

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Why does a paramagnetic sample display greater magnetization (for the same magnetizing field) when cooled?