12th Physics_Magnetism and Matter_Avanti Module

P19 – Magnetism and Matter 24 Fourth Edition P19. Magnetism and Matter TABLE OF CONTENTS P19. Magnetism and Matter 24 P19.1 Bar Magnets.................................................................................................................................................................................25 P19.2 Earth’s Magnetism .....................................................................................................................................................................29 P19.3 Magnetisation of Materials.....................................................................................................................................................32 Subjective Questions..............................................................................................................................................................................36 Test Practice Problems .........................................................................................................................................................................37 Answer Key ................................................................................................................................................................................................41

P19 – Magnetism and Matter 25 PRE-TEST Q1. If ���⃗��� = 4������̂, ���⃗⃗��� = 2������̂, then what is the value of ���⃗��� × ���⃗⃗���? Q2. The magnitude of magnetic field due to a circular coil at its center is zero. (True/False) Q3. The magnitude of electric field of a dipole of moment ���⃗��� on its equatorial position at a distance of ������ from its center is given by __________. Q4. The angle between two vectors whose dot product is zero would be __________. Q5. Magnitude of magnetic permeability in vacuum is equal to 4������ × 10−7. (True/False) PRE-REQUISITE 1. Vectors & Calculus 2. Magnetic Effects of Electric Current 3. Electrostatics P19.1 Bar Magnets CONCEPTS 1. Bar magnet and its geometrical parameters 2. Magnetic moment of a bar magnet 3. Force, Torque and Potential Energy related to bar magnets in a uniform magnetic field 4. Effect of combining, bending or cutting on the magnetic moment and pole strength of bar magnets PRE-READING Category Book Name Chapter Section 5 5.1 to 5.3 REQUIRED NCERT Class 12 Physics Part 1 36 36.1, 36.4 Optional HC Verma Part 2 PRE-READING EXERCISE Q1. Magnetic field lines in a bar magnet are the same as the electric field lines in an electric dipole (True/False) Q2. Magnitude of magnetic field due to a pole of strength ������ at a distance of ������ from it is given by __________. Q3. Torque on a magnetic dipole of moment ���⃗⃗���⃗ in a magnetic field ���⃗⃗��� is __________. Q4. Magnetic moment is a (scalar /vector) quantity. Q5. Magnetic moments can be added vectorially to obtain net magnetic moment. (True/False)

P19 – Magnetism and Matter 26 IN CLASS EXERCISE LEVEL 1 Q1. A short bar magnet has a length 2������ and a magnetic moment 10 ������������2. Find the magnitude of magnetic field at a distance of ������ = 0.1 ������ from its center on the axial line. Here, ������ is negligible as compared to ������. Q2. A short bar magnet experiences a torque of magnitude 0.64 ������������ when it is placed in a uniform magnetic field of 0.32 ������, taking an angle of 30° with the direction of the field. Find the magnetic moment of the magnet. Q3. The magnitude of force between two magnetic poles is ������. If the distance between the poles and pole strengths of each pole is doubled, then find the magnitude of the force experienced in the new situation. LEVEL 2 Q4. A magnetic dipole is under the effect of two magnetic fields inclined at 75° to each other. One of the fields has a magnitude of 1.5 × 10−2 ������. The magnet comes to a stable position at an angle of 30° with the direction of the above field in between both the fields. What is the magnitude of the other field. Q5. A magnet of length 14 ������������ and magnitude of magnetic moment ������ is broken into two parts of lengths 6 ������������ and 8 ������������. They are put at right angle to each other with opposite poles together. What is the magnitude of magnetic moment of the combination. Q6. A magnet with magnitude of magnetic moment 2������ ������−1 is aligned in the direction of magnetic field of magnitude 0.1 ������. What is the net work done to bring the magnet normal to the magnetic field? Q7. What would be the magnitude of the net magnetic moment of the system shown in the figure? Q8. A magnet of length 0.1 ������ and pole strength 10−4 ������������ is kept in a magnetic field of 30 ������������ ������−2 magnitude at an angle of 30°. Find the magnitude of torque acting on it. LEVEL 3 Q9. Two identical magnetic dipoles with magnitude of magnetic moment 2 ������ ������2 are placed at a separation of 2 ������ with their axis perpendicular to each other in air. What is the magnitude of resultant magnetic field at a mid- point between the dipoles? Q10. Find the magnitude of magnetic induction at ������, for the arrangement shown in the figure, when two similar short magnets with magnitudes of magnetic moment ������ are joined at the middle so that they are mutually perpendicular. P19.1

P19 – Magnetism and Matter 27 Q11. A bar magnet when placed at an angle of 300 to the direction of magnetic field induction of intensity 5 × 10−2 ������, experiences a moment of magnitude 25 × 10−6 ������������. If the length of the magnet is 5 ������������, then find its pole strength. HOMEWORK LEVEL 1 Q1. A short bar magnet placed with its axis at 300 with a uniform external magnetic field of 0.16 ������ magnitude experiences a torque of magnitude 0.032 ������������ . What would be the magnitude of magnetic moment of the bar magnet? Q2. Consider a short magnetic dipole of magnetic length 10 ������������. What would be its geometric length? Q3. A magnet of magnetic moment of magnitude 20 CGS units is freely suspended in a uniform magnetic field of intensity 0.3 CGS units. What is the amount of work done in deflecting it by an angle of 30° in CGS units? LEVEL 2 Q4. A magnetized wire with magnitude of magnetic moment ������ and length ������ is bent in the form of a semicircle of radius ������. Then what would be the magnitude of its magnetic moment. Q5. Derive the expression for the magnetic field due to short bar magnet of magnetic dipole moment ������ and length 2������, on the axis at a distance ������ (where ≫ ������ ) from the centre of the magnet. Q6. If a magnet having a pole strength ������ is cut into four equal parts such that their lengths as well as breadths are equal and half of the actual dimensions of the actual magnet. What would the pole strength of each new part be? Q7. If a magnet having a magnitude of magnetic moment ������ is cut into four equal parts such that their lengths as well as breadths are equal and half of the actual dimensions of the actual magnet. What would the magnitude of magnetic moment of each new part be? Q8. If a bar magnet of length ������ and cross-sectional area ������ is cut into two equal parts along the line as shown in the figure, then how does the pole strength of each pole change? A) Half B) Double C) One-fourth D) Four times Q9. The effective length of a magnet is 31.4 ������������ and its pole strength is 0.5 ������������. Calculate its magnitude of magnetic moment. If it is bent in the form of a semicircle, then what would its magnitude of magnetic moment be? Q10. A steel wire of length ������ has a magnitude of magnetic moment ������. It is bent in ������-shape at its mid-point. What is the new magnitude of magnetic moment.

P19 – Magnetism and Matter 28 LEVEL 3 Q11. ������ and ������√3 are the magnitudes of magnetic dipole moments of the two magnets which are joined to form a cross figure. What is the inclination of the system with the field, if their combination is suspended freely in a uniform external magnetic field ���⃗⃗��� as shown in the figure below. Q12. Two small magnets each with magnitudes of magnetic moment ������0 is placed parallel to each other (as shown in the figure). Find the magnetic field at point O. Q13. Two short magnets with magnitudes of magnetic moment 2 ������������2 and 5 ������������2 are placed along two lines drawn at right angle to each other on the sheet of paper as shown in the figure. What is the magnetic field intensity at the point of intersection of their axis? Q14. Two small bar magnets with magnitude of magnetic moment ������ each are arranged at the opposite corners of a square of side ������, such that their centers coincide with the corners and their axes are parallel. If the like poles are in the same direction, find the magnitude of magnetic induction at any of the other corners of the square. P19.1

P19 – Magnetism and Matter 29 P19.2 Earth’s Magnetism CONCEPTS 1. Origin of Earth's Magnetism 2. Relation between geographical and magnetic poles of the Earth 3. Components of Earth’s Magnetic field and the parameters associated with it 4. Construction and working of a Dip Circle 5. Tangent Galvanometer PRE-READING Category Book Name Chapter Section 5.4 REQUIRED NCERT Class 12 Physics Part 1 5 36.6-36.8 REQUIRED HC Verma Part 2 36 PRE-READING EXERCISE Q1. Magnetic field arising due to electric currents produced by convection motion of metallic fluids in the outer core of the earth is called __________ effect. Q2. The angle between the geographical axis and the magnetic axis of the earth is __________. Q3. The angle between the magnetic meridian and the geographical meridian at a point is known as the __________. Q4. The angle formed by the net magnetic field at a plane which is not the magnetic meridian with the horizontal component of the magnetic field on that plane is known as the (true/apparent) dip. Q5. The angle formed by the net magnetic field in the magnetic meridian with the horizontal component of the magnetic field is known as the (true/apparent) dip. Q6. Angle of dip is also known as the angle of inclination. (True/False) IN CLASS EXERCISE LEVEL 1 Q1. At a certain place the angle of dip is 30° and the horizontal component of earth’s field is 0.5 Oersted, then find the magnitude of earth’s total magnetic field in Oersted. Q2. The coil in a tangent galvanometer is 16 ������������ in radius. If a current of 20 ������������ is to produce a deflection of 45°, then what is the number of turns wound on it? (Take horizontal component of earth’s magnetic field = 0.36 × 10−4 ������ and ������0 = 4������ × 10−7 ������������ ������−1 ������−1) Q3. The radius of the coil of a tangent galvanometer which has 10 turns is 0.1 ������. Find the current required to produce a deflection of 60° (������������ = 4 × 10−5������).

P19 – Magnetism and Matter 30 LEVEL 2 Q4. A compass needle with magnitude of magnetic moment 60 ������������2 pointing towards geographical north at a place where the horizontal component of earth’s magnetic field is 40 ������������������ ������−2 experiences a torque of magnitude 1.2 × 10−3������������. What is the declination at the place? Q5. Two small magnets A and B with magnitudes of dipole moments ������0 and 2 ������0 respectively are fixed perpendicular to each other with their north poles in contact. The combination is placed on a floating body so as to move freely in earth’s magnetic field (as shown in figure). Find the value of ������. LEVEL 3 Q6. The plane of dip circle is set in the geographical meridian and the apparent dip is ������1. It is then set in a vertical plane perpendicular to the geographical meridian. The apparent dip becomes ������2. Find the angle of declination ������. Q7. A short bar magnet with magnitude of magnetic moment 25 ������������−1 is placed with its axis perpendicular to earth’s field direction. At what distance from the center of the magnet, the resultant field is inclined at 45° with earth’s field, if the horizontal component of earth’s magnetic field, ������ = 0.4 × 10−4 ������? Take the angle of dip = 00 at the position of the bar magnet. HOMEWORK LEVEL 1 Q1. The angle between magnetic meridian and geographical meridian is known as A) Magnetic dip B) Magnetic latitude C) Magnetic declination D) Magnetic longitude Q2. The angle of dip at a place is 37° and the vertical component of the earth’s magnetic field is 6 × 10−5 ������. What is the magnitude of earth’s magnetic field at this place. (tan 37° = 3) 4 Q3. The magnetic needle of a tangent galvanometer is deflected at an angle of 30° due to a current in its coil. If the horizontal component of earth’s magnetic field is 0.314 × 10−4 ������, then find the magnitude of magnetic field at the center of the coil due to the current. LEVEL 2 Q4. A bar magnet 20 ������������ in length is placed with its south pole towards geographical north. The neutral points are situated at a distance of 40 ������������ from the centre of the magnet. If the horizontal component of the earth’s magnetic field, ������ = 3.2 × 10−5 ������������������������������/������������������������������2 then find the pole strength of the magnet. Assume the angle of dip to be 00. Q5. A dip circle is so that its needle moves freely in the magnetic meridian. In this position, the angle of dip is 40°. Now the dip circle is rotated so that the plane in which the needle moves makes an angle of 30° with the magnetic meridian. In this position, the needle will dip by an angle A) 40° B) 30° C) More than 40° D) Less than 40° Q6. A tangent galvanometer has a reduction factor of 1 ������ and it is placed with the plane of its coil perpendicular to the magnetic meridian. What is the deflection produced when a current of 1 ������ is passed through it? P19.2

P19 – Magnetism and Matter 31 Q7. Two tangent galvanometer having coils of the same radius are connected in series. Same current flowing in them produces deflections of 60° and 45° respectively. What is the ratio of the number of turns in the coil? LEVEL 3 Q8. A dip circle shows an apparent dip of 60° at a place where the true dip is 45°. If the dip circle is rotated through 90°, find the apparent dip at this new position. Q9. If ������1 and ������2 be the apparent values of the dip observed in two planes at right angles to each other and ������ is the true value of the dip, then: A) sin2 ������ = sin2 ������1 + sin2 ������2 B) cot2 ������ = cot2 ������1 + cot2 ������2 C) tan2 ������ = tan2 ������1 + tan2 ������2 D) cos2 ������ = cos2 ������1 + cos2 ������2

P19 – Magnetism and Matter 32 P19.3 Magnetisation of Materials CONCEPTS 1. Magnetic Intensity, Intensity of Magnetization, Magnetic Susceptibility, Magnetic flux density and Magnetic permeability 2. Hysteresis curve 3. Paramagnetic, Ferromagnetic and Diamagnetic materials 4. Curie’s temperature for different materials 5. Curie/Weiss Law PRE-READING Category Book Name Chapter Section REQUIRED NCERT Class 12 Physics Part 1 5 5.5 to 5.7 OPTIONAL HC Verma Part 2 37 37.1-37.9 PRE-READING EXERCISE Q1. An example of a paramagnetic material is (Aluminum/Calcium/Sodium/All). Q2. Type of materials which exhibit perfect conductivity and perfect diamagnetism are called __________. Q3. In diamagnetic substances, the net dipole moment in the atom is __________. Q4. The value of ������ at which ������ = 0 in a hysteresis curve is called __________. Q5. The phenomenon of perfect diamagnetism in superconductors is called __________ effect. IN CLASS EXERCISE LEVEL 1 Q1. In the hysteresis cycle, the value of ������ needed to make the intensity of magnetization zero is called A) Retentivity B) Coercive force C) Lorentz force D) None of the above Q2. When a ferromagnetic material is heated to temperature above its curie point, the material A) Is permanently magnetized B) Remains ferromagnetic C) Behaves like a diamagnetic D) Behaves like a paramagnetic Q3. For a paramagnetic material, what is the dependence of the magnetic susceptibility ������ on the absolute temperature? Q4. At a temperature of 27°������ , the susceptibility of a ferromagnetic material is found to be ������ . What would its susceptibility be at 327°������? Q5. A diamagnetic material has magnetic susceptibility ������ which is: A) ������ = 0 B) 0 < ������ < 1 C) ������ > 1 D) ������ < 0 P19.3

P19 – Magnetism and Matter 33 Q6. To shield an instrument from the external magnetic field, it is placed inside a cabin made from: A) Wood B) Ebonite C) Iron D) Diamagnetic substance Q7. Permanent magnets are made of steel because steel has A) Low retentivity and low coercive field B) High retentivity and high coercive field C) Low retentivity and high coercive field D) High retentivity and low coercive field LEVEL 2 Q8. The magnetic susceptibility of a paramagnetic substance at −73° ������ is 0.0060, then what is the value of magnetic susceptibility at −173°������? Q9. A paramagnetic substance of susceptibility 3 × 10−4 is placed in a magnetic field of 4 × 10−4 ������������−1. Then find the intensity of magnetization in the units of ������������−1. Q10. The magnetic susceptibility of a material of a rod is 499. The absolute permeability of vacuum is 4������ × 10−7 ������������−1. Find the absolute permeability of the material rod. LEVEL 3 Q11. A sample of paramagnetic salt contains 2.0 × 1024 atomic dipoles each of dipole moment 1.5 × 10−23 JT−1. The sample is placed under a homogeneous magnetic field of 0.64 ������, and cooled to a temperature of 4.2 ������. 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 ������ and a temperature of 2.8 ������? (Assume Curie’s law) HOMEWORK LEVEL 1 Q1. A permanent magnet: A) Attracts all substances B) Attracts only magnetic substances C) Attracts magnetic substances and repels all non-magnetic substances. D) Repels all non-magnetic substances Q2. When a diamagnetic substance is brought near north or south pole of a bar magnet, it is: A) Attracted by the poles B) Repelled by the poles C) Attracted by North Pole and repelled by South Pole. D) Repelled by North Pole and attracted by South Pole Q3. Large transformers, when used for some time, become very hot and are cooled by circulating oil. The heating of the transformers is due to: A) The heating effect of the current alone B) Hysteresis loss alone C) Both Hysteresis loss and Heating effect of the current D) The intense sunlight at noon Q4. The susceptibility of paramagnetic substance is: A) Very large B) Positive C) Positive and small D) Negative and small

P19 – Magnetism and Matter 34 Q5. The susceptibility of diamagnetic substance is: A) Very large B) Positive and small C) Negative and small D) Zero Q6. The susceptibility of a ferromagnetic substance is: A) Positive and large B) Positive and very small C) Negative and very large D) None of the above. Q7. Liquid oxygen remains suspended between two poles of a magnet, because it is: A) Diamagnetic B) Paramagnetic C) Ferromagnetic D) Antiferromagnetic Q8. Above curie temperature: A) A paramagnetic substance becomes ferromagnetic. B) A ferromagnetic substance becomes paramagnetic. C) A paramagnetic substance becomes diamagnetic. D) A diamagnetic substance becomes paramagnetic LEVEL 2 Q9. If the B-H curves of two samples of ������ and ������ of iron are as shown below, then which one of the following statements is correct? A) Both ������ and ������ are suitable for making permanent magnet B) ������ is suitable for making permanent magnet and ������ for making electromagnet C) ������ is suitable for making electromagnet and ������ for making permanent magnet D) Both ������ and ������ are suitable for making electromagnet LEVEL 3 Q10. Electrical resistance of certain materials, known as superconductors, changes abruptly from a non-zero value to zero as their temperature is lowered below a critical temperature ������������(0). An interesting property of super conductors is that their critical temperature becomes smaller than ������������(0) if they are placed in a magnetic field i.e., the critical temperature ������������(������) is a function of the magnetic field strength ������. The dependence of ������������(������) on ������ is as shown in the figure. In the graphs below, the resistance ������ of a superconductor is shown as a function of its temperature ������ for two different magnetic fields ������1 (solid line) and ������2(dashed line). If ������2 is larger than ������1, which of the following graphs shows the correct variation of ������ with ������ in these fields? P19.3

P19 – Magnetism and Matter 35 A) B) C) D) Q11. A superconductor has ������������(0) = 100 ������. When a magnetic field of 7.5 Tesla is applied, its ������������ decreases to 75 K. For this material one can definitely say that when (Note: T=Tesla) A) ������ = 5 ������, ������������(������) = 80 ������ B) ������ = 5 ������, 75������ < ������������(������) < 100 ������ C) ������ = 10 ������, 75 ������ < ������������(������) < 100 ������ D) ������ = 10 ������, ������������(������) = 70 ������

P19 – Magnetism and Matter 36 Subjective Questions Q1. A proton has spin and magnetic moment just like an electron. Why then is its effect neglected in magnetism of materials? Q2. Discuss the classification of materials based on their behaviour in magnetic field. Q3. A bar magnet of magnetic moment m and moment of inertia I (about centre, perpendicular to length) is cut into two equal pieces, perpendicular to length. Let T be the period of oscillations of the original magnet about an axis through the mid-point, perpendicular to length, in a magnetic field B. What would be the similar period T′ for each piece? Q4. Define magnetization and explain magnetic intensity. Q5. Explain angle of declination. Q6. What is the origin of earth’s magnetic field. Q7. Explain angle of dip. Q8. What are the three major components of earth’s magnetic field? Q9. Why does a paramagnetic sample display greater magnetization (for the same magnetizing field) when cooled? Q10. Why is diamagnetism, in contrast, almost independent of temperature? Q11. If a toroid uses Bismuth for its core, will the field in the core be (slightly) greater or (slightly) lesser than when the core is empty? Q12. Is the permeability of a ferromagnetic material independent of the magnetic field? If not, is it more for lower or higher fields? Q13. 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? Q14. Would the maximum possible magnetization of a paramagnetic sample be of the same order of magnitude as the magnetization of a ferromagnet? Subj.

P19 – Magnetism and Matter 37 Test Practice Problems No. of questions: 25 Total time: 75 mins Time per question: 3 mins Purpose: To practice a mixed bag of questions in a speed based format similar to what you will face in entrance examinations. In most entrance examinations, you will get not more than 3 minutes to attempt a question. Hence, you need to be able to attempt a question in less than 3 minutes, and at the end of 3 minutes skip the question and move to the next one. Approach:  Attempt the Test Practice Problems only when you have the stipulated time available at a stretch.  Start a timer and attempt the section as a test.  DO NOT look at the answer key / solutions after each question.  DO NOT guess a question if you do not know it. Competitive examinations have negative marking.  Fill the table at the end of the TPP and evaluate the number of attempts, and accuracy of attempts, which will help you evaluate your preparedness level for the chapter. Q1. If a bar magnet is placed with its north pole pointing towards magnetic north of earth, the neutral points are located: A) On the axial line B) On the equatorial line C) On the line making an angle ������ with axis, where ������ can have any value D) On the line making an angle of 45° with axis Q2. A dip circle lies initially in the magnetic meridian. If it is now rotated through angle ������ in the horizontal plane, then tangent of the angle of apparent dip to the tangent of the true dip is: A) 1: cos ������ B) cos ������ : 1 C) 1: sin ������ D) sin ������ : 1 Q3. The angle of dip at a place where horizontal and vertical components of earth’s magnetic field are equal is: A) Zero B) 45° C) 90° D) 30° Q4. At the magnetic north pole of the earth , the value of the horizontal component of earth’s magnetic field ������ and the angle of dip ������ is A) ������ = 0, ������ = 45° B) ������ = 0, ������ = 0° C) ������ = 0, ������ = 90° D) ������ = 1, ������ = 45° Q5. At 45° to the magnetic meridian the apparent dip is 60°. The true dip A) tan−1 √3 B) tan−1 1 C) tan−1 √3 D) tan−1 √1 √3 2 6 Q6. A person is facing magnetic north. An electron in front of him flies horizontally towards the north and deflects towards east. He is in/at: A) Northern hemisphere B) Southern hemisphere C) Equator D) Cannot be predicted Q7. Alnico is preferred for making permanent magnet due to its A) High retentivity, low coercive field B) Low retentivity, high coercive field C) Low retentivity, low coercive field D) High retentivity, high coercive field

P19 – Magnetism and Matter 38 Q8. Soft iron is preferred as core of transformer in the form of sheets due to its: A) High retentivity, low coercivity and low hysteresis loss B) High retentivity, high coercivity and low hysteresis loss C) Low retentivity, low coercivity and high hysteresis loss D) High retentivity, low coercivity and high hysteresis loss Q9. The magnetic fields at two points lying at same distance from an isolated pole are: A) The same both in magnitude and direction B) Different both in magnitude and direction C) The same in magnitude and different in directions D) Different in magnitude but same in direction Q10. A long magnet is cut into two parts in such a way that the ratio of their lengths is 2:1. The ratio of pole strengths of both the sections is: A) Equal B) 2:1 C) 1:2 D) 4:1 Q11. There is no couple acting when two bar magnets are placed coaxially since A) There are no forces on the poles B) The forces are parallel to each other C) The forces are parallel and lines of action do not coincide with each other D) None of these Q12. If a magnet is divided into 2������ parts by cutting along lines parallel to length, then pole strength of each part will be: A) Same B) 1 times C) 1 times D) 1 times ������ 2������ 4������ Q13. A magnetic needle is kept in a non-uniform magnetic field. It experiences: A) A force but not a torque B) A force and a torque C) Neither a force nor a torque D) A torque but not a force Q14. Needles ������1, ������2 and ������3 are made of a ferromagnetic, a paramagnetic and a diamagnetic substance respectively. A magnet when bought close to them will: A) Attract ������1 and ������2 strongly but repel ������3 B) Attract ������1 strongly, ������2 strongly but repel ������3 C) Attract ������1 strongly but repel ������2 and ������3 weakly D) Attract all three of them Q15. Isoclinic are the lines joining the places of: A) Equal dip B) Equal declination C) Equal value of H D) Equal dip and declination both Q16. Isogonic lines represent the lines of: A) Zero declination B) Equal declination C) Equal dip D) Equal horizontal field Q17. Agonic lines are lines joining places of: A) Zero declination B) Equal declination C) Zero dip D) Equal dip Q18. Aclinic lines are lines joining places of: A) Zero declination B) Equal declination C) Zero dip D) Equal dip T.P.P.

P19 – Magnetism and Matter 39 Q19. A dip needle shows angle of dip ������ when the dip circle is placed in magnetic meridian. Now, the dip circle is rotated by an angle ������ and the apparent angle of dip at this place is ������’, then (tan ������′) is tan ������ A) 1 B) 1 C) cos ������ D) sin ������ cos ������ sin ������ Q20. A tangent galvanometer has a coil with 50 turns and radius equal to 4 ������������. A current of 0.1 ������������������ is passing through it. The plane of the coil is set parallel to the earth’s magnetic meridian. If the value of the earth’s horizontal component of the magnetic field is 7 × 10−5������ and ������0 = 4������ × 10−7������������/������ - ������ , then the deflection in the galvanometer needle will be A) 45° B) 48.2° C) 50.7° D) 52.7° Q21. Angle of dip ������ and latitude ������ on earth’s surface are related as A) tan ������ = 2 tan ������ B) tan ������ = cot ������ C) tan ������ = tan ������ D) tan ������ = tan ������ 2 Q22. Period of oscillation of a bar magnet in earth’s magnetic field is ������. If its mass is reduced to one-fourth of the original mass, maintaining all other parameters same, the new time period will be A) ������ B) 2������ C) (������) D) (������) 2 4 Q23. Two bar magnets of the same mass, length and breadth but having magnetic moments ������ and 2������ are joined together pole for pole and suspended by a string. The time period of the assembly in a magnetic field of strength ������ is 3 sec. If now the polarity of one of the magnets is reversed and the combination is again made to oscillate in the same field, the time period of oscillation (in second) will be A) 6 B) 3 C) 3√3 D) √3 Q24. A bar magnet, held horizontally, is set into angular oscillations in the earth’s magnetic field. Its time periods are ������1 and ������2 at two places where the angle of dip are ������1 and ������2, respectively, The ratio of the resultant magnetic fields at these two places will be A) ������1 sin ������1 : ������2 sin ������2 B) ������1 cos ������1 : ������2 cos ������2 C) ������22 sin ������2 : ������12 sin ������1 D) ������22 cos ������2 : ������12 cos ������1 Q25. A bar magnet oscillates with a frequency of 10 oscillations per minute. When another bar magnet is placed on its axis at a small distance, it oscillates at 14 oscillations per minute. Now, the second bar magnet is turned so that poles are instantaneous, keeping the location same. The new frequency of oscillation will be A) 2 vibrations/min B) 4 vibrations/min C) 10 vibrations/min D) 14 vibrations/min

P19 – Magnetism and Matter 40 DATA ANALYSIS Guide A # of questions Total problems in TPP B # Attempts Total attempts in OMR C # Correct Total questions correct D # Incorrect Out of the ones marked in OMR E # Unattempted ������ − ������ F Percentage attempts G Percentage Accuracy ������ ������ × 100 ������ ������ × 100 Question type # Correct (C) # Incorrect (I) # Unattempted (U) Level 1 Level 2 Level 3 Tip: To begin with, your accuracy must be high, typically > 60%. Percentage attempts should be > 50% As time progresses, your percentage attempts should increase without a reduction in accuracy. Additionally, you should be able to get > 80% Easy questions correct, as they involve basic recall of the concepts and formulae of the chapter. T.P.P.

P19 – Magnetism and Matter 41 Answer Key PRE-TEST Q3. − ���������⃗��� Q1. 8���̂��� ������3 Q2. False Q4. 90° Q5. True P19.1 BAR MAGNETS PRE-READING EXERCISE LEVEL 2 HOMEWORK Q8. A LEVEL 1 Q9. 0.157 ������������2, 0.1 ������������2 Q1. False Q4. 15 × 10−2������ Q1. 0.4 ������������/������ Q10. ������ Q2. 12 ������������ Q2. ������0 ������ √2 Q3. 3(2 − √3) ������������������ √2 4������ ������2 Q5. 5������ Q3. ���⃗⃗���⃗ × ���⃗⃗��� 7 Q4. Vector LEVEL 3 Q6. 0.2 ������ Q5. True Q11. 60° Q7. √3 ������������ Q8. 1.5 × 10−4 ������������ LEVEL 2 Q12. 0 IN CLASS EXERCISE LEVEL 3 Q4. 2������ Q13. 3.99 × 10−4 ������ LEVEL 1 ������ ������0 ������ Q1. 2 × 10−3������ 4������ ������3 Q2. 4 ������������2 Q9. 2√5 × 10−7 ������ Q5. ������0 2������ ���̂��� Q14. Q3. ������ 4������ ������3 Q10. μ0M √5 Q6. ������ Q11. 4πd3 2 2 × 10−2������������ Q7. ������ 4 PRE-READING EXERCISE P19.2 EARTH’S MAGNETISM LEVEL 2 Q1. Dynamo Q4. 51.2 ������ ������ Q2. 11.30 LEVEL 2 Q5. C Q3. Angle of Declination Q4. 30° Q6. 45° Q4. Apparent Q5. tan−1(2) Q7. √3 Q5. True Q6. True LEVEL 3 1 Q6. tan−1 (tan ������1) IN CLASS EXERCISE LEVEL 3 LEVEL 1 tan ������2 Q1. 1 Oersted Q8. cot−1 √2 Q7. 0.5 ������ √3 3 HOMEWORK Q2. 458 LEVEL 1 Q9. B Q3. 1.1 ������ Q1. C Q2. 10−4 ������ Q3. 1.81 × 10−5 ������

P19 – Magnetism and Matter 42 P19.3 MAGNETISATION OF MATREIALS PRE-READING EXERCISE Q6. C Q2. B Q1. All Q7. B Q3. C Q2. Superconductors Q4. C Q3. Zero LEVEL 2 Q5. C Q4. Retentivity Q8. 0.0120 Q6. A Q5. Meissner Q9. 12 × 10−8 ������������−1 Q7. B Q10. 2������ × 10−4 ������������−1 Q8. B IN CLASS EXERCISE LEVEL 1 LEVEL 3 LEVEL 2 Q1. B Q11. 7.9 JT−1 Q9. B Q2. D Q3. ������ = 1/������ HOMEWORK LEVEL 3 Q4. 0.5������ LEVEL 1 Q10. A Q5. D Q1. B Q11. B TEST PRACTICE PROBLEMS Q. No. Ans. Level Mark (C) / (I) / (U) Q. No. Ans. Level Mark (C) / (I) / (U) as appropriate as appropriate HARD MEDIUM Q1. B MEDIUM Q13. B MEDIUM Q2. A EASY Q14. B EASY Q3. B MEDIUM Q15. A EASY Q4. C MEDIUM Q16. B EASY Q5. C HARD Q17. A EASY Q6. A EASY Q18. C MEDIUM Q7. D EASY Q19. A HARD Q8. A MEDIUM Q20. B HARD Q9. C EASY Q21. A EASY Q10. A MEDIUM Q22. C HARD Q11. C MEDIUM Q23. C MEDIUM Q12. C Q24. D HARD Q25. A Ans.