Q.1. Answer the following questions regarding earth’s magnetism.
(a) A vector needs three quantities for its specification. Name the three independent quantities conventionally used to specify the earth’s magnetic field.
(b) The angle of dip at a location in southern India is about 180. Would you expect a grater or lesser dip angle in Britain ?
(c) If you made a map of magnetic field lines at Melbourne in Australia, would the lines seem to go into the ground or come out of the ground ?
(d) Which direction would a compass needle point to, if located right on the geomagnetic north or south pole ?
(e) The earth’s field, it is claimed, roughly approximates the field due to a dipole of magnetic moment 8 × 1022 JT-1 located at its Centre. Check the order of magnitude of this number in some way.
(f) Geologists claim that besides the main magnetic n-s poles, there are several local poles on the earth’s surface oriented in different directions. How is such a thing possible at all ?
Sol. (a) The three independent quantities used to specify earth’s magnetic field are.
(c) As Melbourne is situated in southern hemisphere where north pole of earth’s magnetic field lies, therefore, magnetic lines of force seem to come out of the ground.
(d) At the poles, earth’s field is exactly vertical. As the compass needle is free to rotate in a horizontal plane only, it may point out in any direction.
(e) Here, M = 8 × 1022 JT-1
Let us calculate magnetic field intensity at magnetic equator of earth, i.e., at a point on equatorial line of short magnetic dipole for which, d = R = radius of earth = 6400 km = 6.4 × 106 m.
Thus value is in good approximation with the observed values of earth’s magnetic field.
(f) The earth’s magnetic field is only approximately a dipole field. Therefore local N-S poles exist oriented in different directions. This is possible due to deposits of magnetized minerals.
Q.2. Answer the following questions : (a) The earth’s magnetic field varies from point to point in space. Does it also change with time ? If so, on what time scale does it change appreciably ?
(b) The earth’s core is known to contain iron. Yet geologists do not regard this as a source of earth’s magnetism, why ?
(c) The charged currents in the outer conducting regions of earth’s core are thought to be responsible for earth’s magnetism. What might be the battery to sustain these currents ?
(d) The earth may have even reversed the direction of its field several time during its history of 4 to 5 billion years. How can geologists know about the earth’s field in such distant past ?
(e) The earth’s field departs from its dipole shape substantially at large distances (greater than about 30000 km). What agencies may be responsible for this distortion ?
(f) Interstellar space has an extremely weak magnetic field of the order of 10-12 T. can such a weak field be of any significant consequence? Explain.
Sol. (a) Yes, earth’s field undergoes a change with time. For example, daily changes, annual changes, secular changes with period of the order of 960 years and irregular changes like magnetic storms. Time scale for appreciable change is roughly a few hundred years.
(b) The earth’s core does contain iron but in the molten form only. This is not ferromagnetic and hence it cannot be treated as a source of earth’s magnetism.
(c) One of the possibilities is the radioactivity in the interior of the earth. But it is not certain.
(d) Earth’s magnetic field gets recorded weakly in certain rocks during their solidification. An analysis of these rocks may reveal the history of earth’s magnetism.
(e) The earth’s magnetic field gets modified by the field produced by motion of ions in earth’s ionosphere.
(f) When a charged particle moves in a magnetic field, it is deflected along a circular path such that
When B is low, R is high, i. e., radius of curvature of path is very large. Therefore, over the gigantic inter stellar distance, the deflection of charged particles becomes less noticeable.
A magnetic field develops along the axis of the solenoid. Therefore, the current carrying solenoid behaves like a bar magnet.
Q.7. A bar magnet of magnetic moment 1.5 JT-1 lies aligned with the direction of a uniform magnetic field of 0.22 T.
(a) What is the amount of work done to turn the magnet so as to align its magnetic moment
(i) normal to the field direction, (ii) opposite to the field direction ?
(b) What is the torque on the magnet in cases (i) and (ii)n?
Q.8. A closely wound solenoid of 2000 turns and area of cross section 1.6 × 10-4 m2, carrying a current of 4 amp. Is suspended through its Centre allowing it to turn in a horizontal plane :
(a) What is the magnetic moment associated with the solenoid ?
(b) What are the force and torque on the solenoid if a uniform horizontal magnetic field of 7.5 10-2 T is set up at an angle of 300 with the axis of the solenoid ?
The earth’s field lies in a vertical plane 120 west of geographic meridian at an angle of 600 above the horizontal.
Q.15. A short bar magnet of magnetic moment 5.2 × 10-2JT-1 is placed with its axis perpendicular to earth’s field direction. At what distance form the Centre of the magnet, is the resultant field inclined at 450 with earth’s field on (i) its normal bisector, (ii) its axis ? Magnitude of earth’s field at the place 0.42 G. Ignore the length of the magnet in comparison to the distances involved.
Q.16. Answer the following questions :
(a) Why does a paramagnetic sample display greater magnetisation (for the same magnetistising field) when cooled.
(b) Why is diamagnetism, in contrast, almost independent of temperature ?
(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 ?
(d) Is the permeability of a ferromagnetic material independent of the magnetic field ? If not, is it more for lower or higher fields ?
(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 ?
(f) Would the maximum possible magnetisation of a paramagnetic sample be of the same order of magnitude as the magnetisation of a ferromagnet ?
Sol. (a) This is because at lover temperatures, to tendency to disrupt the alignment of dipoles (due to
(b) In a diamagnetic sample, each molecule is not a magnetic dipole in itself. Therefore, random thermal motion of molecules does not affect the magnetism of the specimen. That is why diamagnetism is independent of temperature.
(c) As bismuth is diamagnetic, therefore, the field in the core will be slightly less than when the core is empty.
(d) No, Permeability of a ferromagnetic material is not independent of magnetic field. As is clear form the hysteresis curve, is greater for lower fields.
(e)Magnetic field lines are always nearly normal to the surface of a ferromagnet at every point. The proof of this important fact is based on the boundary conditions of magnetic fields (B and H) at the interface of two media. The magnetic permeability of a ferromagnetic material µ >> 1. That is why the field lines meet this medium normally.
(f) Yes, maximum possible magnetisation of a paramagnetic sample will be of the same order of magnitude as the magnetisation of a ferromagnet. The saturation however, requires very high magnetising fields, which are hard to achieve.
Q.17. Answer the following questions : (a) Explain qualitatively on the basis of domain picture, the irreversibility in the magnetisation curve of a ferromagnet.
(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 ?
(c) A system displaying a hysteresis loop such as a ferromagnet is a device for strong memory? Explain the meaning of this statement.
(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 ?
(e) A certain region of space is to be shielded from magnetic fields. Suggest a method.
(b) As energy dissipated per cycle is directly proportional to the area of the hysteresis loop, therefore, carbon steel piece will dissipate greater heat energy.
(c) Magnetisation of a ferromagnet depends not only on the magnetising field, but also on the history of magnetisation (i.e., how many cycles of magnetisation it has undergone. Tues value of magnetisation of a specimen is a record of memory of the cycles of magnetisation it has undergone. The system displaying such a hysteresis loop can thus act as a device for storing memory.
(d) The ceramic materials (specially treated barium, iron oxides) also called ferrites are used for coating magnetic tapes as memory tapes in a cassettly player, or for building memory stores in a modern computers.
(e) A space can be shielded from magnetic field by surrounding the space with soft iron ring. As magnetic field lines will be drawn into the ring, the enclosed region will become free of magnetic filed.
Strength of magnetic field on this line due to current in theLet the neutral points lie at a distance r from the cable.
Q.20. A compass needle free to turn in a horizontal plane is placed at the centra of a circular coil of 30 turns and radius 12 cm. The coil is in a vertical plane making an angle of 450 with the magnetic meridian whin the current in the coil is 0.35 amp., the needle points west to east,
(a) Determine the horizontal component of earth’s magnetic field at the location.
(b) The current in the coil is reversed and the coil is rotated about its vertical axis by an angle of 900 in the anticlockwise sense looking from above. Predict the direction of the needle. Take the magnetic declination at the places to be zero.
Q.21. A monoenergetic (18 ke V) electron beam initially in the horizontal
Direction is subjected to a hori- zontal magnetic field of 0.40 G normal to the initial direction. Estimate the up or down deflection of 150 with this field, what is the magnitude of the other filed ?
In a magnetic field, electron beam is deflected along a circular arc of radius r,
Q.25. The magnetic moment vectors associated with the intrinsic spin angular momentum and orbital angular momentum 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.