5.25) The magnetic moment vectors and associated with the intrinsic spin angular momentum S and orbital angular momentum l, respectively, of an electron, are predicted by quantum theory (and verified experimentally to a high accuracy) to be given by:
Which of these relations is in accordance with the result expected classically? Outline the derivation of the classical result.
5.24. A Rowland ring of mean radius 15 cm has 3500 turns of wire wound on a ferromagnetic core of relative permeability 800. What is the magnetic field B in the core for a magnetising current of 1.2 A?
5.23. A sample of paramagnetic salt contains atomic dipoles each of dipole moment The sample is placed under a homogeneous magnetic field of 0.64 T, and cooled to a temperature of 4.2 K. The degree of magnetic saturation achieved is equal to . What is the total dipole moment of the sample for a magnetic field of 0.98 T and a temperature of 2.8 K? (Assume Curie’s law)
5.22) A monoenergetic (18 keV) electron beam initially in the horizontal direction is subjected to a horizontal magnetic field of 0.04 G normal to the initial direction. Estimate the up or down deflection of the beam over a distance of 30 cm . [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 the electron beam from the electron gun to the screen in a TV set.]
5.21. A magnetic dipole is under the influence of two magnetic fields. The angle between the field directions is , and one of the fields has a magnitude of T. If the dipole comes to stable equilibrium at an angle of with this field, what is the magnitude of the other field?
20 (b). A compass needle free to turn in a horizontal plane is placed at the centre of circular coil of 30 turns and radius 12 cm. The coil is in a vertical plane making an angle of with the magnetic meridian. When the current in the coil is 0.35 A, the needle points west to east. The current in the coil is reversed, and the coil is rotated about its vertical axis by an angle of in the anticlockwise sense looking from above. Predict the direction of the needle. Take the
magnetic declination at the places to be zero.
5.20(a). A compass needle free to turn in a horizontal plane is placed at the centre of circular coil of 30 turns and radius 12 cm. The coil is in a vertical plane making an angle of with the magnetic meridian. When the current in the coil is 0.35 A, the needle points west to east. Determine the horizontal component of the earth’s magnetic field at the location.
5.19 A telephone cable at a place has four long straight horizontal wires carrying a current of 1.0 A in the same direction east to west. The earth’s magnetic field at the place is 0.39 G, and the angle of dip is . The magnetic declination is nearly zero. What are the resultant magnetic fields at points 4.0 cm below the cable?
5.18. A long straight horizontal cable carries a current of 2.5 A in the direction south of west to north of east. The magnetic meridian of the place happens to be west of the geographic meridian. The earth’s magnetic field at the location is 0.33 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.)
17 (d). What kind of ferromagnetic material is used for coating magnetic tapes in a cassette player, or for building ‘memory stores’ in a modern computer?
17 (c) ‘A system displaying a hysteresis loop such as a ferromagnet, is a device for storing memory?’ Explain the meaning of this statement.
17 (b). 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?
17 (a). Explain qualitatively on the basis of domain picture the irreversibility in the magnetisation curve of a ferromagnet.
16 (f). Would the maximum possible magnetisation of a paramagnetic sample be of the same order of magnitude as the magnetisation of a ferromagnet?
5. 16 (e). 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?
5. 16 (d). Is the permeability of a ferromagnetic material independent of the magnetic field? If not, is it more for lower or higher fields?
5.16 Answer the following questions
(c). 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?
A short bar magnet of magnetic movement is placed with its axis perpendicular to the earth’s field direction. At what distance from the centre of the magnet, the resultant field is inclined at 45° with earth’s field on its normal bisector.
5.16 Answer the following questions
(b). Why is diamagnetism, in contrast, almost independent of temperature?