Magnetism and Matter
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5.6 If the solenoid in Exercise 5.5 is free to turn about the vertical direction and a uniform horizontal magnetic field of 0.25 T is applied, what is the magnitude of torque on the solenoid when its axis makes an angle of 30° with the direction of applied field?
5.6 If the solenoid in Exercise 5.5 is free to turn about the vertical direction and a uniform horizontal magnetic field of 0.25 T is applied, what is the magnitude of torque on the solenoid when its axis makes an angle of 30° with the direction of applied field?
5.6 Magnetic field strength, B = 0.25 T
Magnetic moment, M = 0.6 J/T
The angle , between the axis of the solenoid and the direction of the applied field is 30 . Therefore, the torque acting on the solenoid is given as
= 0.6 = 7.5 J
Upvote 
5.5 A closely wound solenoid of 800 turns and area of cross section 2.5 × 10–4 m2 carries a current of 3.0 A. Explain the sense in which the solenoid acts like a bar magnet. What is its associated magnetic moment?
5.5 A closely wound solenoid of 800 turns and area of cross section 2.5 × 10–4 m2 carries a current of 3.0 A. Explain the sense in which the solenoid acts like a bar magnet. What is its associated magnetic moment?
5.5 Number of turns, n = 800
Area of the cross-section, A = 2.5
Current flowing, I = 3.0 A
A current carrying solenoid behaves like a bar magnet because a magnetic field develops along its axis (along the length).
The magnetic moment associated is calculated as M = nIA = 800 2.5 J/T= 0.6 J/T
Upvote 5.4 A short bar magnet of magnetic moment m = 0.32 JT–1 is placed in a uniform magnetic field of 0.15 T. If the bar is free to rotate in the plane of the field, which orientation would correspond to its (a) stable, and (b) unstable equilibrium? What is the potential energy of the magnet in each case?
5.4 A short bar magnet of magnetic moment m = 0.32 JT–1 is placed in a uniform magnetic field of 0.15 T. If the bar is free to rotate in the plane of the field, which orientation would correspond to its (a) stable, and (b) unstable equilibrium? What is the potential energy of the magnet in each case?
5.4 Moment of the bar magnet, M = 0.32 J/T
Magnetic field, B = 0.15 T
The bar magnet is aligned along the magnetic field. This system is considered as being in stable equilibrium. Hence, the angle , between the bar magnet and the magnetic field is 0 .
Potential energy of the system = -MBcos = - 0.
Upvote 5.3 A short bar magnet placed with its axis at 30° with a uniform external magnetic field of 0.25 T experiences a torque of magnitude equal to 4.5 × 10–2 J. What is the magnitude of magnetic moment of the magnet?
5.3 A short bar magnet placed with its axis at 30° with a uniform external magnetic field of 0.25 T experiences a torque of magnitude equal to 4.5 × 10–2 J. What is the magnitude of magnetic moment of the magnet?
5.3 Magnetic field strength, B = 0.25 T
Torque on the bar magnet, = 4.5 J
Angle between the bar magnet and the external magnetic field, = 30
From the relation T = MB , where M = Magnetic moment, we get
M = = = 0.36 J/T
Hence the magnetic moment is 0.36 J/T
Upvote 5.2 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 the earth’s magnetism. Why?
(c) The charged currents in the outer conducting regions of the earth’s core are thought to be responsible for earth’s magnetism. What might be the ‘battery’ (i.e., the source of energy) to sustain these currents?
(d) The earth may have even reversed the direction of its field several times 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 30,000 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.
[Note: Exercise 5.2 is meant mainly to arouse your curiosity. Answers to some questions above are tentative or unknown. Brief answers wherever possible are given at the end. For details, you should consult a good text on geomagnetism.]
5.2 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 the earth’s magnetism. Why?
(c) The charged currents in the outer conducting regions of the earth’s core are thought to be responsible for earth’s magnetism. What might be the ‘battery’ (i.e., the source of energy) to sustain these currents?
(d) The earth may have even reversed the direction of its field several times 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 30,000 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.
[Note: Exercise 5.2 is meant mainly to arouse your curiosity. Answers to some questions above are tentative or unknown. Brief answers wherever possible are given at the end. For details, you should consult a good text on geomagnetism.]
5.2 (a) Earth's magnetic field changes with time. It takes a few hundred years to change by an appreciable amount. The variation in earth's magnetic field with the time cannot be neglected.
(b) Earth's core contains molten iron. This form of iron is not ferromagnetic. Hence this is not considered as
Upvote 5.1 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 18°. Would you expect a greater or smaller 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) In which direction would a compass free to move in the vertical plane 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 J T–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?
5.1 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 18°. Would you expect a greater or smaller 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) In which direction would a compass free to move in the vertical plane 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 J T–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?
5.1 (a) Earth’s magnetic field can be specified by three following independent quantities
Magnetic declination
Angle of dip
Horizontal component of earth’s magnetic field.
(b) The angle of dip at a point depends on how far the point is located with respect to North pole or South pole. The angle of dip
Upvote The net magnetic flux through any closed surface is zero, according to Gauss's Law for magnetism.
Mathematically,
? B · dA = 0.
It states that all magnetic field lines that enter a surface must exit from it as well. In this way, it is different from the electric charges which can exist independently a
Upvote The Earth's magnetic field makes a magnetic inclination or dip with the horizontal plane at a particular location. It shows how much the magnetic field is tilted from the horizontal. It gets tilted due to the Earth's magnetic nature. The formula is:
tan I = B_V / B_H,
where B_V is the vertical compon
Upvote What is magnetic declination and why is it important?
What is magnetic declination and why is it important?
The angle between the magnetic north (the direction a compass points) and the geographic north (true north) is the magnetic declination. This angle can change over time due to changes in the Earth's magnetic field and varies with location on Earth. It is important for navigation where accurate direc
Upvote The Earth's magnetic field makes a magnetic inclination or dip with the horizontal plane at a particular location. It shows how much the magnetic field is tilted from the horizontal. It gets tilted due to the Earth's magnetic nature. The formula is:
tan I = B_V / B_H,
where B_V is the vertical compon
Upvote