2nd PUC Physics Question Bank Chapter 5 Magnetism and Matter

Karnataka 2nd PUC Physics Question Bank Chapter 5 Magnetism and Matter

2nd PUC Physics Magnetism and Matter NCERT Text Book Questions and Answers

Question 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, is 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 the magnetic moment 8 x 1022 JT-1 located at its center. 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?
(a)

1. The angle of dip or magnetic inclination, δ Galvanometer resistance, G = 12 Q The galvanometer can be converted into the voltmeter of range 0 to V (here V = 18 V) by connecting a high series resistance R given by
2. Magnetic declination, θ
3. The horizontal component of the magnetic field of earth BH.

(b) It is about 70° in Britain because it is closer to the magnetic north pole of the earth.

(c) The magnetic field lines due to the magnetism of earth would seem to come out of the ground at Melbourne in Australia because this region is in the Southern hemisphere of the earth where the north pole of the earth’s magnet lies.

(d) Compass can point in any direction because it is free to move in the horizontal plane but at magnetic poles, the magnetic field of the earth is exactly vertical so there will be no horizontal component of the magnetic field to effect the compass.

(e) The magnetic field at a point on the equatorial line of the magnetic dipole (earth as a magnetic dipole) is given by,

It is really of the order of the observed field of the earth.

(f) Because of the deposit of magnetic materials, at different places, there can be different local poles.

Question 2.
(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 a 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 1012 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.]
(a) Although appreciable change can take a few hundred years yet change with time is very much there.

(b) Molten iron has a temperature more than Curie temperature so it is not ferromagnetic in nature.

(c) Probably radioactivity (i.e. emission of a, P, and y particles from the nuclei) present in the interior of the earth is responsible for it.

(f) During the solidification of some rocks, the magnetic field of the earth gets weakly recorded in these rocks. The geomagnetic history of these rocks can be traced by making an analysis of such rocks.

(e) Ionosphere of the earth consists of charged ions. The motion of these ions causes a magnetic field which affects the magnetic field of the earth at large distances from earth. The magnetic field due to ions depends upon extraterrestrial disturbances like solar wind.

(f) A weak field of the order of 10-12 T can cause the charged particles to move along circular paths of very large radii. Over a small distance, we may not be able to notice the deflection in the path of the charged particles but over a large interstellar distance, the distance is quite noticeable.

Question 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 x 10-2 What is the magnitude of the magnetic moment of the magnet?

Question 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?
m = 0.32 JT-1, B = 0.15 T
(a) The bar magnet is directed along the direction of external field so that PE is minimum, U = – mB = – 4.8 x 10-2J (most stable)
(b) Any other position, other than the above is unstable. The one with maximum PE is with the field antiparallel to that of the magnet. In this case
Umax = mB = 4.8 x 10-2J

Question 5.
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?
Using M = NIA, we get
M = 800 x 3 x 2.5 x 10-4 = 0.60 JT-1.
The sense is determined by the direction of the current.

Question 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 the torque on the solenoid when its axis makes an angle of 30° with the direction of the applied field?
B = 0.25 T, θ = 30°
τ = mB sin θ
= 0.6 x 0.25 x sin 30
= 0.6 x 0.25 x $$\frac { 1 }{ 2 }$$
= 0.075 Nm (or J)

Question 7.
A bar magnet of magnetic moment 1.5 J T-1 lies aligned with the direction of a uniform magnetic field of 0.22 T.
(a) What is the amount of work required by an external torque 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)?
(a) M = 1.5 J-1
B = 0.22 T
The work done to rotate the magnet from the position θ1 to θ2 is given by
MB(cos θ1 – cos θ2)
(i) θ1=0° , θ2 = 90°
∴ W = 1.5 x 0.22 (cos0°-cos 90°)
= 1.5 x 0.22 (1-0)= 1.5 x 0.22
= 0.33 J

(ii) θ1 =0° θ2 = 180°
∴ W = 1.5×0.22 (cos0° – cos 180°)
= 1.5 x 0.22 (1-(-1))
= 1.5 x 0.22×2
= 0.665 J

(b) The torque acting on the magnet is given by
τ= MB sin θ
θ = 90°
τ = 1.5 x 0.22 x sin 90°
=1.5 x 0.22×1
= 0.33 Nm
θ = 180°

Question 8.
A closely wound solenoid of 2000 turns and area of cross-section 1.6 × 10-4 m2carrying 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 10-2 T is set up at an angle of 30° with the axis of the solenoid?
(a) Using M = NIA, we get
M = 2000 x 4 x 1.6 x 10-4
= 1.28 Am2
The direction of M is as per the sense of current using the right-handed rule.

(b) Torque, x = MB sin 0
= 1.28 x 7-5 x 10-2 x sin 30°
= 4.8 x 10-2 N m
Force is zero because of uniform field.

Question 9.
A circular coil of 16 turns and radius 10 cm carrying a current of 0.75 A rests with its plane normal to an external field of magnitude 5.0 x 10-2 The coil is free to turn about an axis in its plane perpendicular to the field direction. When the coil is turned slightly and released, it oscillates about its stable equilibrium with a frequency of 2.0 s-1. What is the moment of inertia of the coil about its axis of rotation?
a = 10 cm = 0.1 m
n = 16
I = 0.75 A
B = 5 x 10-2T
V = 2 s-1            .
The magnetic moment associated with the coil, M = n l A
= nl x πa2
= 16 × 0.75 x n x(0.1)2 = 0.377 Am2
If I is a moment of inertia of the coil about its axis of rotation, then its frequency of oscillation is given by,

Question 10.
A magnetic needle free to rotate in a vertical plane parallel to the magnetic meridian has its north tip pointing down at 22° with the horizontal. The horizontal component of the earth’s magnetic field at the place is known to be 0.35 G. Determine the magnitude of the earth’s magnetic field at the place.

Question 11.
At a certain location in Africa, a compass points 12° west of the geographic north. The north tip of the magnetic needle of a dip circle placed in the plane of magnetic meridian points 60° above the horizontal. The horizontal component of the earth’s field is measured to be 0.16 G Specify the direction and magnitude of the earth’s field at the location.

Thus, the earth’s magnetic field has a magnitude of 0.32 G and lies in a vertical plane 12° west of the geographic medium making an angle of 60° (upwards) with the horizontal.

Question 12.
A short bar magnet has a magnetic moment of 0,48 J T-1. Give the direction and magnitude of the magnetic field produced by the magnet at a distance of 10 cm from the centre of the magnet on
(a) The axis,
(b) The equatorial lines (normal bisector) of the magnet.
M = 0.48 J T-1

Question 13.
A short bar magnet placed in a horizontal plane has its axis aligned along the magnetic north-south direction. Null points are found on the axis of the magnet at 14 cm from the centre of the magnet. The earth’s magnetic field at the place is 0.36 G and the angle of dip is zero. What is the total magnetic field on the normal bisector of the magnet at the same distance as the null-point (i.e., 14 cm) from the centre of the magnet? (At null points, the field due to a magnet is equal and opposite to the horizontal component of the earth’s magnetic field.)
In this position of the magnet, the null points lie on its axial line.
At the null point, Baxial =BH
Let M be the magnetic dipole moment of the magnet, Then

At the same distance on the normal bisector (equatorial line) of the magnet, the magnetic field due to the short bar magnet,

Question 14.
If the bar magnet in exercise 5.13 is turned around by 180°, where will the new null points be located?
In this position of the magnet, the null points lie on its equatorial line,
At the null point, Bequi = BH
Let M be the magnetic dipole moment of the magnet and r. be the distance of the null point from the centre of the magnet.

Question 15.
A short bar magnet of magnetic moment 5.25 x 10-2 J T 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 the earth’s field on
(a) its normal bisector and
(b) its axis. The magnitude of the earth’s field at the place is given to be 0.42 G. Ignore the length of the magnet in comparison to the distances involved.

(i) On its normal bisector:
Fig (1) shows the point P on the normal bisector of the magnet, where the resultant magnetic field B is inclined at 45°, with the earth’s field.
It can happen only if Bequi is equal to the horizontal component of the earth’s field (BH)

Fig (2) shows the point P on the axis of the magnet, where the resultant field is inclined at 45° with the earth’s magnetic field.

2nd PUC Physics Magnetism and Matter Additional Exercises

Question 16.
(a) Why does a paramagnetic sample display greater magnetization (for the same magnetizing 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 magnetization of a paramagnetic sample be of the same order of magnitude as the magnetization of a ferromagnet?
(a) At lower temperatures, the tendency of dealignment of magnetic dipoles with magnetising field is reduced because of a decrease in their random thermal motion.

(b) The induced dipole moment in a diamagnetic sample is opposite to the magnetising field irrespective of the internal thermal motion of the atoms. Thus, diamagnetism is independent of the changes in temperature.

(c) It will be slightly less because bismuth is a diamagnetic substance.

(d) No, the permeability of a ferromagnetic material depends upon the applied magnetic field. Its value is large for the small values of the applied field.
The graph between B and H is of the shape as shown:

It follows that value B is quite large for a comparatively small value of H.

(e) When two media are considered and one of these has μ >> 1, then magnetic field lines meet normally to this medium. Proof of this fact is available from the boundary conditions of magnetic fields (strength of magnetic field B and magnetising intensity H) at the interface of two media.

(f) The maximum possible magnetisation of a paramagnetic sample would be of the same order of magnitude as the magnetisation of a ferromagnetic sample but the paramagnetic sample requires a very high magnetising field which may not be practically possible.

Question 17.
(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 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.
(a) It can be observed from the given curve that magnetisation persists even when the external field is removed. This reflects the irreversibility of a ferromagnet.
(b) Heat dissipated per second is directly proportional to the area of the hysteresis loop so carbon steel piece will dissipate greater heat energy.
(c) Magnetisation of a ferromagnet depends upon the applied field as a number of cycles of magnetisation given to it. Thus the value of magnetisation can indicate the number of cycles of magnetisation a sample has undergone or in other words, the memory with respect to the cycles stands stored in the sample.
(d) Ceramics are used for this purpose. Ferrites which are specially treated barium iron oxides are commonly used.
(e) The space to be shielded is enclosed by soft iron rings. The magnetic field lines remain confined in the ferromagnetic material of the rings and the enclosed space will be free from the magnetic effect.
Note: Magnetic shielding is not as effective as electrostatic shielding is.

Question 18.
A long straight horizontal cable carries a current of 2.5 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 G, and the angle of dip is zero. Locate the line of neutral points (ignore the thickness of the cable). (At neutral points, the magnetic field due to a current-carrying cable is equal and opposite to the horizontal component of earth’s magnetic field.)
The magnetic N-S line is 10° west of the geographical N-S line as shown in the figure. The straight horizontal cable x y is 10° north of the east.

Here,
δ=0° and B = 0.33 G
The horizontal component of the earth’s field

= 0.33 G = 0.33 x 10-4 T At a point below the cable, the direction of the magnetic field produced is same as that of BH, while at a point above the cable, a neutral point lies above the cable. If the distance of the neutral point from the wire is ‘a’, then

Question 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 35°. The magnetic declination is nearly zero. What are the resultant magnetic fields at points 4.0 cm below the cable?
The earth’s magnetic field, B = 0.39 G;
δ = 35°
Therefore, the horizontal component of the earth’s magnetic field,

Resultant field below the cable:
According to the right-hand thumb rule, the direction of b’ at a point below the cable will be opposite to BH.
Therefore, at a point 4 cm above the cable,
B’H = BH + B’
= 0.3195 + 0.2
= 0.5195 G
Bv = 0.2237 G
Therefore, the resultant magnetic field above the cable,

Question 20.
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 45° with the magnetic meridian. When the current in the coil is 0.35 A, the needle points west to east.
(A) Determine the horizontal component of the 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 90° in the anti-clockwise sense looking from above. Predict the direction of the needle. Take the magnetic declination at the places to be zero.
(a) The horizontal component of the earth’s magnetic field (BH) acts along the magnetic N – S line. As the coil is placed in a vertical plane making angle of 45° with the magnetic meridian, the magnetic field B produced by the coil on passing current through it, will be along normal to the plane of the coil, in a direction making an angle of 45° with the W-E line. The compass needle placed at the centre of the coil points west to east.

Question 21.
A magnetic dipole is under the influence of two magnetic fields. The angle between the field directions is 60°, and one of the fields has a magnitude of 1.2 x 10-2 If the dipole comes to stable equilibrium at an angle of 15° with this field, what is the magnitude of the other field?

B1= 1.2 × 10-2 T
The inclination of the dipole with Bl, θ = 15°
Therefore, inclination of the dipole with B2
θ2 = 60 – 15 = 45°
As the dipole is in equilibrium; the torque on the dipole due to the filed B1 is equal and opposite to that due to B2.
If M is the magnetic dipole moment of the dipole, then,
MB1 sin θ1= MB2 sin θ2

Question 22.
A monoenergetic (18 keV) electron beam initially in the horizontal direction is subjected to a horizontal magnetic field of 0.04G normal to the initial direction. Estimate the up or down deflection of the beam over a distance of 30 cm (me = 9.11 x 10-31 kg). [Note: Data in this exercise are so chosen that the answer will give you an Idea of the effect of the earth’s magnetic field on the motion of the electron beam from the electron gun to the screen in a TV set.]

suppose that the electron moves along a circular path of radius r under the effect of the magnetic field. Then

Figure shows an electron covering a circular path PQ C = 30 cm = 0.3 m and of radius OP = OQ= 11.32m

It follows the electron will undergo a deflection PA in a downward direction, while it covers a distance PQ. IF θ is angle subtended by PQ

Question 23.
A sample of paramagnetic salt contains 2.0 x 1024 atomic dipoles each of dipole moment 1.5 x 10-23 JT-1. 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 15%. 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)

Question 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?

Question 25.
The magnetic moment vectors µs and µ, associated with the intrinsic spin angular momentum S and orbital angular momentum 1, respectively, of an electron, are predicted by quantum theory (and verified experimentally to a high accuracy) to be given by:
µs=-(e/m)S,
µ1=- (e/ 2m) l,
Which of these relations is in accordance with the result expected classically? Outline the derivation of the classical result.
The relation $$\vec { { \mu }_{ 1 } } =(-e/2m)\vec { L }$$
is in accordance with the classical physics. It can be derived classical as below:
An electron revolving in an orbit of radius r is associated with magnetic moment.

2nd PUC Physics Magnetism and Matter Competitive Exam Questions and Answers

Question 1.
The magnetic lines of force inside a bar magnet:
(A) Are from north-pole to south-pole of the magnet
(B) Do not exist
(C) Depend upon the area of cross-section of a bar magnet
(D) Are from south-pole to north-pole of the magnet
(D) Are from south-pole to north-pole of magnet

Question 2.
A magnetic needle is kept in a non-uniform magnetic field. It experiences
(A) A torque but not a force
(B) Neither a force nor a torque
(C) A force but not a torque
(D) A force and a torque
(D) A force and a torque

Question 3.
The dimensions of magnetic field intensity in M, L, T and C is given as
(A) MT-2 C-1
(B) MLT-1 C-1
(C) MT-2 C-2
(D) MT-1 C-1
(D) MT-1 C-1

Question 4.
Relative permeability and permeability of a material are er and pr respectively. Which of the following values of these quantities are allowed for a diamagnetic material?
(A) ∈r = 1.5, µr = 1.5
(B) ∈r =0.5, µr =1.5
(C) ∈r =1.5, µr =0.5
(D) ∈r =0.5, µr = 0.5 .
(C) ∈r =1.5, µr =0.5

Question 5.
Domain formation is the necessary feature of
(A) Diamagnetism.
(B) Paramagnetism
(C) Ferromagnetism
(D) all of these
(C) Ferromagnetism

Question 6.
The magnetic moment has dimensions of
(A) [LA]
(B) [L2A]
(C) |LT-1A|
(D) [L2T-1A]
(B) [L2A]

Question 7.
The angle of dip is 90° at
(A) Poles
(B) Equator
(C) Both (A) and (B)
(D) None of these
(A) Poles

Question 8.
The magnetic moment (µ) of a revolving electron around the nucleus varies with principal quantum number as
(A) µ α n
(B) $$\mu \alpha \frac { 1 }{ n }$$
(C) $$\mu \quad \alpha \quad { n }^{ 2 }$$
(D) $$\mu \alpha \frac { 1 }{ { n }^{ 2 } }$$
(A) µ α n

Question 9.
Which of the following is not suitable for the core of the electromagnets?
(A) Cu-Ni alloy
(B) Soft iron
(C) Steel
(D) Air