Bihar Board - Class 12 Physics - Chapter 5: Magnetism And Matter Long Answer Question
Long Answer Type Questions
1. Draw magnetic field lines when a
(i) diamagnetic,
(ii) paramagnetic substances are placed in an external magnetic field.
Which magnetic property distinguishes this behavior of the field lines due to the two substances?
Answer:
(i) When a diamagnetic material is placed in an external magnetic field.
(ii) When a paramagnetic material is placed in an external magnetic field.
Magnetic susceptibility distinguishes this behavior of the field lines due to the two substances.
2. Depict the behavior of magnetic field lines when
(i) a diamagnetic material and
(ii) a paramagnetic material is placed in an external magnetic field. Mention briefly the properties of these materials which explain this distinguishing behavior.
Answer: Diamagnetic materials: Diamagnetic materials are those which have tendency to move from stronger to the weaker part of the external magnetic field.
Examples: Bismuth, copper, lead and silicon.
Properties:
(i) When a rod of diamagnetic material is sus-pended inside a magnetic field, it slowly sets itself at right angles to the direction of the field.
(ii) When a diamagnetic material is placed inside a magnetic field, the magnetic field lines become slightly less dense in the diamagnetic material.
(iii) For diamagnetic material :
-1‘m <0 , 0r<1 , <0
Paramagnetic materials: Paramagnetic materials are those which get weakly magnetized when placed in an external magnetic field. They have a tendency to move from a region of weak magnetic field to strong magnetic field.
Examples: Aluminum, sodium, calcium and oxygen.
Properties :
(i) When a rod of paramagnetic material is suspended inside a magnetic field, it slowly sets itself parallel to the direction of the magnetic field.
(ii) When a paramagnetic material is placed inside a magnetic field, the magnetic field lines become slightly more dense in the paramagnetic material.
(iii) The magnetic susceptibility ‘m‘ of a paramagnetic material has a small positive value,
i.e. 0 < ‘m< ε
3. Define the following using suitable diagrams :
(a) magnetic declination and
(b) angle of dip. In what direction will a compass needle point when kept at the
(i) poles and
(ii) equator?
Answer:
Magnetic declination:
Angle between magnetic meridian and geographical meridian
Angle of dip : It is the angle which the magnetic needle makes with the horizontal in the magnetic meridian.
Direction of the compass needle is vertical to the earth’s surface at poles.
Parallel to the earth’s surface at equator.
4. Write two characteristic properties each to select materials suitable for
(i) permanent magnets and
(ii) electromagnets.
Answer:
Properties of a material—
(a) For making a permanent magnet:
High retentivity
High coercivity
High permeability
(b) For making an electromagnet:
High permeability .
Low retentivity
Low coercivity
5. What is induced magnetism? Discuss “Attraction is preceded by induction”.
Answer: Induced magnetism :
The magnetism acquired by a magnetic substance when kept near a magnet is called induced magnetism. When a piece of iron or steel AB is placed near in contact with a magnet it is found to be magnetized i.e. it acquires the property of attracting small iron filings if brought near its end B. If the magnet is now removed, all the iron filings fall down. Thus the steel piece behaves like a magnet so long as it is in the neighborhood of the magnet.
A magnetic pole induces an opposite polarity on the nearer end of the iron piece and a similar polarity on the end far from it. In fact attraction on the iron piece is due to the induction by the magnet. This attraction is always preceded by induction.
6. What are the uses of studying hysteresis curves of substance?
Or
What would be your consideration while making electromagnets?
Answer:
Uses of hysteresis curve: Fig. shows two hysteresis curves, one for steel and other for iron. We find that retentivity of soft iron is higher than steel and coercivity of steel is higher than soft iron. These properties are used for making permanent magnets, core of transformers and electromagnets etc.
(i) For permanent magnets: Permanent magnets should have a high value of retentivity (to have a large force of attraction for magnetic materials) and coercivity (to remain magnetic for a long time). But coercivity is more important than retentivity. Hence steel is preferred to iron. Now some alloys like alnico, cobalt, steel are developed which have high value of retentivity and coercivity for making permanent magnets.
(ii) For electromagnets: Electromagnets are used for lifting heavy iron materials and are continuously subjected to cyclic changes. So the materials used for electromagnets must have a high value of retentivity and small hysteresis loss. Hence soft iron is preferred to steel.
(iii) Core of the transformer: The core of the transformer (telephone diaphragms and chokes etc.) continuously undergoes many cycles of magnetisation in one second. So we use the material which has less hysteresis loss. So soft iron is used for cores of transformers, chokes etc.
7. Distinguish between diamagnetic, paramagnetic and ferromagnetic substances.
Answer: Diamagnetic substances are those in which the individual molecule/atom/ion do not possess any net magnetic moment of their own. When placed in a magnetic field they move from stronger part of the field to the weaker part of the field i.e., these are repelled by the magnetic field.
Examples of diamagnetic substances are copper, antimony, bismuth, gold, quartz, mercury etc.
Paramagnetic substances are those in which the individual molecule/atom/ion has a net non-zero magnetic moment of its own. When a paramagnetic substance is placed in an external magnetic field induction B, it tends to align the individual dipole in the direction of the field.
Examples of paramagnetic substances are aluminum, platinum, chromium, chrome, glass etc.
Ferromagnetic substances are those in which each molecule/atom/ion has a non-zero magnetic moment. Individual magnetic moments interact with each other in such a way to align themselves, spontaneously in a common direction. All molecular dipole moments in a domain are lined up resulting in some dipole moments.
When a ferromagnetic substance is placed in an external magnetic field, magnetic moments of different domains are aligned and the material gets strongly magnetized in the direction of the field.
Some examples are iron, cobalt, nickel etc.
8. Two identical iron bars A and B are given, one of which is definitely known to be magnetized. How would you ascertain, whether or not both are magnetized? If only one is magnetized?
Answer: Since repulsion is the sure test of magnetisation, because if bar A attracts the other bar B, then both may be magnets (i.e. their unlike poles are facing each other) or one bar may be a simple piece of iron, but if there is a force of repulsion between them, then both bars must be magnetized.
To know which one is magnetized, place the bar A on the table and bring one end of bar B near the two ends and at the middle of bar A. If there is force of attraction only at the ends of bar A, then bar A is magnetized and B is not magnetized and if there is force of attraction both at the ends as well as at the middle, then bar B is magnetized and A is unmagnetised.
9. Why are permanent magnets made of steel and not of soft iron?
Answer: The so-called permanent magnets are made of hard steel or special alloys. The properties of soft iron and of hard steel are quite different, i.e they have contrasting responses to attempts to make magnets out of them. It is not easy to make a magnet out of a steel rod. but it can be done by placing it in the North-South direction and repeatedly hammering it. Once it has become a magnet in this way, it retains this property unless heated to a high temperature. Our picture of what happens is this: inside the steel there are many small ’atomic’ magnets (like so many compass needles), initially all oriented in random direction; the repeated hammering tends to make them all align themselves in the direction of the earth’s field
On the other hand, filings (long thin pieces) of soft iron do easily become magnets themselves when placed in a magnetic field, for instance near a permanent magnet, but just as easily lose this property when removed. It is a case of "easy come easy go "
10. Compare magnetic properties of soft iron and steel.
Answer: Comparison of magnetic properties of soft iron and steel:
Property | Soft Iron | Steel |
1. Saturation magnetisation (Imax) | more (good for strong magnets) | less (not good for strong magnets) |
2. Retentivity | more but unstable (good for electromagnets) | less but stable (good for permanent magnets) |
3. Coercivity | less (not good for durable magnets) | more (good for durable magnets) |
4.Hysteresis loss | less (good for transformer and choke cores and telephone diaphragms) | more (not good for repeated magnetisation) |
11. (a) Define Magnetic Field, Magnetic Intensity (or magnetic field at a point). What is the S.I. unit of magnetic intensity?
(b) Define a uniform magnetic field. How is it represented geometrically?
Answer: (a) Magnetic Field
The space around a magnet or a current carrying conductor in which the magnetic effect can be felt is called the magnetic field.
Magnetic Intensity
The strength of magnetic field or magnetic intensity at a point is the force experienced by a unit north pole placed at that point. The direction of the field is the direction in which this pole begins to move if free to do so. Thus magnetic intensity is a vector quantity and has both magnitude and direction. The S.I. unit of magnetic intensity is tesla or ampere meter. If a magnetic pole of strength m units placed at a point where the magnetic intensity is B then it experiences a force of m B
(b) Uniform Magnetic Field :
A magnetic field is said to be uniform if a unit isolated north pole placed at different points in the field experiences the same force in the same direction.
Graphically, a uniform magnetic field is represented by equidistant and mutually parallel lines.
12. A bar magnet of magnetic moment 6J/T is aligned at 60° with a uniform external magnetic field of 0.44 T. Calculate (a) the work done in turning the magnet to align its magnetic moment.
(i) normal to the magnetic field,
(ii) opposite to the magnetic field and
(iii) the torque on the magnet in the final orientation in case (ii).
Answer:
Given M = 6 JT-1,
1= 60°,
B = 0.44 T
Since W = MB (cos 1 - cos 2)
(a) (i) 2 = 90°
∴ W = 6 x 0.44 [cos 60° - cos 90°]
= 2.64( 12-0) = 1.34 J
(ii) 2 = 180°
∴ W = 6 x 0.44 [cos 60° - cos 80°]
= 2.64[ 12-1] = 2.64 x 32 = 3.9 J
(b) = MB sinπ = MB.0 = 0.
13. (a) What are magnetic lines of force?
(b) Do the lines of force really exist?
(c) Mention important properties of magnetic lines of force.
Answer:
(a) Magnetic Lines of Force
(i) Imagine a small north magnetic pole is placed in the magnetic field created by a magnet, it will experience a force. The north pole will move under the influence of magnetic field. The path traced by a north pole free to move under the influence of magnetic field is called a magnetic line of force.
(ii) A line of force is a continuous curve in the magnetic field such that the tangent at any point of it gives the direction of the resultant field at that point.
The concept of magnetic lines of force is also used to represent the magnetic field in a region graphically.
(b) Actually the lines of force do not exist but are hypothetically considered to explain many phenomena in terms of lines of force.
(c) Properties of lines of force:
- They are closed and continuous curves.
- They always start from the N-pole and terminate at the S-pole of the magnet.
- The tangent at any point on a line of force gives the direction of the magnetic field at the point.
- They never intersect one another because if two lines of force intersect, there would be two directions of magnetic field at that point which is impossible.
- They are crowded near the poles where the magnetic field is strong and get separated where the magnetic field becomes weak.
- Parallel and equidistant lines of force represent a uniform magnetic field (such as the earth’s magnetic field in a small region).
- They behave like stretched elastic rubber strings.
14. A short bar magnet placed with its axis at 30° with a uniform external magnetic field of 0.16 T experiences a torque of magnitude 0.032 J.
(a) Estimate the magnetic moment of the magnet.
(b) If the bar were free to rotate, which orientations would correspond to its (i) stable, and (ii) unstable equilibrium? What is its potential energy in the field for cases (i) and (ii)?
Answer: (a) The torque on a magnetic dipole of magnetic moment M in an external field B is
= MB sin θ
where θ is the angle between M and B
Here τ = 0.032 J, B = 0.16 T, θ = 30°
∴ M = 0.0320.1612
M = 0.40 JT-1.
The direction of M is from the south pole of the magnet to its north pole.
(b) Potential energy of a magnetic dipole in an external field B is given by U = - MB
(i) The bar is in stable equilibrium when its magnetic moment m is parallel to B (θ = 0); its potential energy then is minimum:
U = - MB = 0.40 x 0.16 = - 0 064 J
(ii) The bar is in unstable equilibrium when M is antiparallel to B (θ = 180°); its potential energy then is maximum.
15. Compared to a bar magnet and a current – carrying solenoid.
Answer: Comparison of a bar magnet and a solenoid :
Bar magnet:
- It attracts magnetic substances.
- When it is suspended freely it rests in the direction of N – S.
- It has two poles.
- Like poles of magnet repel and unlike poles attract.
Solenoid:
- It also attracts magnetic substances.
- It also rests in the N – S direction if suspended freely.
- It also has two poles.
- Like poles of solenoid also repel and unlike poles attract.
16. Define the magnetic elements of earth’s magnetic field at a place.
Or
Establish relations between elements of earth’s magnetic field?
Answer: Elements of earth’s magnetic field:
The earth’s magnetic field at a place can be completely described by three parameters which are called elements of earth’s magnetic field. They are the declination, dip and horizontal component of earth’s magnetic field.
1. Magnetic declination:
The angle between the geographical meridian and the magnetic meridian at a place is called the magnetic declination (α) at that place, Or, it is the angle which a compass needle (free to swing in a horizontal plan b) makes with the geographic north – south direction.
2. Angle of dip or magnetic inclination:
The angle made by the earth’s total magnetic field B with the horizontal direction in the magnetic meridian is called angle of dip (δ) at any place. Or, it is the angle which a dip needle (free to swing in the plane of the magnetic meridian) makes with the horizontal.
At the magnetic equator, the dip needle rests horizontally so that the angle of dip is zero at the magnetic equator. The dip needle rests vertically at the magnetic poles so that the angle of dip is 90° at the magnetic poles. At all other places, the dip angle lies between 0° and 90°.
3. Horizontal component of earth’s magnetic field:
It is the component of the earth’s total magnetic field B in the horizontal direction in the magnetic meridian. If δ is the angle of dip at any place, then the horizontal component of earth’s field B at that place is given by
BH = Bcosδ
At the magnetic equator,
δ = 0°,BH = Bcos 0°= B
At the magnetic poles,
δ = 90°,BH =5cos90°= 0
Thus the value of BH is different at different places on the surface of the earth.
17. Compare the magnetic properties of soft iron and steel.
Answer: Comparison of magnetic properties of soft iron and steel:
Soft iron:
- In soft iron, greater magnetism can be produced, than steel. Its magnetic nature is greater than steel.
- Soft iron does not retain magnetism for a longer time. Its retaintivity is less.
- The magnetization and demagnetization of soft iron are easy.
- Temporary magnets are made of soft iron.
Steel:
- In steel, less magnetism can be produced than soft iron, its magnetic nature is less than soft iron.
- Steel retains magnetism for a longer time. Its retaintivity is greater than soft iron.
- The magnetization and demagnetization of steel are difficult.
- Permanent magnets are made by soft steels.
18. A solenoid has a core of a material with relative permeability 400. The windings of the solenoid are insulated from the core and carry a current of 2A. If the number of turns is 1000 per meter, calculate (a) H, (b) M, (c) B and (d) the magnetizing current IM.
Solution:
Here n = 1000 tums/m, I = 2A, r = 400
(a) H = nI = 1000 x 2 = 2 x 103 Am-1
(b) M = mH = (r -1)H
= (400 – 1) x 2 x 103 ≈ 8 x 105Am-1
(c) B = μH = r 0H
= 400 x 4π x 10-7 x 2 x 103 T = 1.0T .
(d) As M = nIM
∴ IM= Mn
= 81051000
= 8 x 102 A.
19. Derive an expression for the potential energy of a magnetic dipole placed in a uniform magnetic field at an angle θ with it.
Answer: The torque acting on a magnetic dipole of a moment M held at an angle θ with the
direction of a uniform magnetic field B is given by
= MB sin θ
This torque tends to align the magnetic dipole in the direction of the field. Work has to be done in rotating the dipole against the action of the torque. This work is stored as potential energy of the dipole.
The small amount of work done in rotating the dipole through angle do is given by
δW = dθ = MB sin θ. dθ
Total work done in rotating the dipole from angle 1 to 2 is given by :
W = q1q2MB sin d = MB-cos 12
W= - MB[cos2 – cos1]
When dipole is rotated from 1= 90° to 2 = θ,
then W = -MB[cosθ – cos 90°] = -MB cosθ.
∴ Potential energy of dipole V(=W) = -MB cosθ
20. Define the terms magnetic inclination and horizontal component of earth’s magnetic field at a place. Derive the relationship between the two with the help of a diagram.
Answer: Inclination : The angle between the direction of the earth’s magnetic field at a place and the horizontal is called the angle of inclination at that place.
Horizontal component (H) : The total intensity of the earth’s magnetic field at any point m may be resolved into two rectangular components, one along the horizontal and the other along the vertical direction.
The component of the resultant intensity of the earth’s magnetic field in the horizontal direction in magnetic meridian is called its horizontal component.
It is denoted by H. In Fig., the resultant intensity, i.e., R along AP has been resolved into rectangular components. Clearly the horizontal component,
H = R = cos δ …(i)
and the vertical component
V = R = sin δ …(ii)
Dividing (ii) by (i)
VH = R sin R cos =tan
Squaring (i) and (ii) and adding, we get
H2 +V2 =R2 cos2δ+ R2 sin2δ
H2 +V2 = R2 (cos2δ + sin2δ)
H2 +V2 = R2
R = H2 +V2
21. (a) Why is the plane of the coil of tangent galvanometer set in earth’s magnetic meridian ?
(b) If a compass needle is placed on the magnetic north pole of the earth, then how will it behave ?
Answer: (a) The tangent galvanometer is based on tangent law which requires two uniform magnetic
Fields perpendicular to each other. By keeping the i in the magnetic meridian, the magnetic field produced by the current carrying coil becomes perpendicular to the horizontal component (H) of in’s magnetic field. It is because the magnetic field produced by a current carrying coll is perpendicular to the plane of the coil.
(b) At the magnetic north (or south) pole of the earth, the angle of dip is 90°. Therefore, only the vertical component of earth’s magnetic field acts; the horizontal component of earth’s magnetic field being zero there. Consequently, the compass needle may stay in any direction.
22. A closely wound solenoid of 800 turns and area of cross-section 2.5 x 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?
Solution: N = 800,
A = 2.5 x 10-4 m2,
I = 3.0A,
m = ?
m = ANI = 2.5 x 10-4 x 800 x 3.0
= 7.5 x 8 x 102
= 0.600 A m2
The field of solenoid is uniform along the axis, and for short solenoid, it is similar to that of a bar magnet and the polarity depends on the direction of circulation of current.
23. A closely wound solenoid of 2000 turns and area of cross-section 1.6 x 10-4 m2, carrying a current of 4.0 A, is suspended through its center allowing it to turn in a horizontal plane.
(a) What is the magnetic moment associated with the solenoid?
(b) What is the force and torque on the solenoid if a uniform horizontal magnetic field of 7.5 x 10-2T is set up at an angle of 30° with the axis of the solenoid?
Solution:
Number of turns of the solenoid = 2,000
I = 4A
A= 1.6x 10-4m2
(a) The magnetic moment of the solenoid,
M = (IA) x number of turns
= 4 x 1.6 x 10-4 x 2000
= 1.28 Am2
(b) τ= MB sin θ
B = 7.5 x 10-2T
θ = 30°
τ = 1.28 x 7.5 x 10-2 x sin 30°
= 0.048 Nm
The net force on the solenoid is zero.
24. Answer the following questions.
(a) Explain qualitatively on the basis of domain picture the irreversibility in the magnetization 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 storing 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.
Answer: (a) A ferromagnetic material has many small domains of magnetic field. But the magnetic moments of these domains are distributed in random order so that there is no magnetism in the unmagnetised state. Under the increasing external magnetic field, the domains merge and magnetism increases until saturation is produced.
On reducing the magnetizing field, the merged domains do not split at the rate they merged and hence the retentivity. The domains are not completely randomized even if the external field is brought to zero. This shows the irreversibility in the magnetisation curve of the ferromagnetic material.
(b) Carbon steel piece, because heat lost per cycle is proportional to the area of the hysteresis loop.
(c) Magnetisation of a ferromagnet is not a single-valued function of the magnetizing field. Its value for a particular field depends both on the field and also on the history of magnetisation (i.e., how many cycles of magnetisation it has gone through, etc.).
In other words, the value of magnetisation is a record or memory of its cycles of magnetisation. If information bits can be made to correspond to these cycles, the system displaying such a hysteresis loop can act as a device for storing information.
(d) Ceramics (specially treated barium iron oxides) also called ferrites.
(e) Surround the region by soft iron rings. Magnetic field lines will be drawn into the rings, and the enclosed space will be free of the magnetic field. But this shielding is only approximate, unlike the perfect electric shielding of a cavity in a conductor placed in an external electric field.
25. (a) Is there any importance for the Curie point? Explain.
(b) Define the S.I unit of the magnetic field. “A charge moving at right angles to a uniform magnetic field does not undergo a change in kinetic energy.” Why?
Answer:
(a) When the temperature rises, the susceptibility of ferromagnetic substances decreases. At a certain temperature, its ferromagnetic property completely loses and becomes paramagnetic in nature. The temperature at which the transition from Ferro to para takes place is called Curie point or Curie temperature, e.g. For iron, Curie temp is about 1000 K, for Cobalt – about 1400 K and for Nickel about 631 K.
(b) Tesla is the SI unit of the magnetic field. The magnetic field at a point is one Tesla if a charge of one coulomb while moving perpendicular to the magnetic field with a velocity of 1 ms-1 experiences a force of 1 newton at that point.
The force on a moving charged particle in a magnetic field is perpendicular to its direction of motion. So work done on the charged particle by the magnetic force is zero. Hence the kinetic energy of a charged particle in a magnetic field remains unchanged.
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