Magnetism and Matter: Class 12 Physics Practice Questions

A geologist observes that a rock sample repels a compass needle. Laboratory tests show the sample moves from stronger to weaker field regions between electromagnet poles, has no residual magnetism after field removal, and has susceptibility χ = −0.000085. A solenoid with 500 turns, length 25 cm, and current 2 A uses this material as its core.

A geologist is surveying a region and uses a magnetic compass to navigate. She notices that near a certain rocky outcrop, the compass needle is slightly repelled from the rock surface instead of being attracted to it. She collects a small sample of the rock and takes it to a laboratory. In the lab, the following observations are recorded:
(i) When placed between the poles of a strong electromagnet, the sample moves from the stronger field region to the weaker field region.
(ii) When the external magnetic field is removed, the sample shows no residual magnetism.
(iii) The susceptibility (χ) of the material is measured to be −0.000085.
(iv) A cylindrical bar of this material, wound with N = 500 turns over a length of 25 cm and carrying a current of 2 A, is used as a solenoid core.

Based on this scenario, answer the following:
(a) Identify the magnetic class of the rock sample. Name ONE common example of such a material.
(b) What is the relative permeability (μ_r) of this material? Is it greater than, equal to, or less than 1?
(c) Calculate the magnetisation (M) of the material inside the solenoid. (Given: χ = −0.000085)
(d) The geologist's compass needle is deflected away from the rock. Justify this behaviour using the concept of magnetic susceptibility.

A geologist studies two rock samples near a strong bar magnet. Sample P causes field lines to crowd inside it and aligns parallel to the field (strongly attracted). Sample Q causes field lines to become sparser inside it and aligns perpendicular to the field (weakly repelled).

A geologist is studying rock samples from two different volcanic sites. She places both samples near a strong bar magnet and observes the following:

• Sample P: The field lines around it become denser inside the sample and sparser outside it. When suspended freely on a thread, it aligns itself parallel to the applied field and is attracted towards the stronger region of the field.

• Sample Q: The field lines around it become slightly sparser inside and denser just outside. When suspended freely, it aligns itself perpendicular to the applied field and is weakly repelled from the stronger region.

Based on these observations, answer the following:

(i) Identify the magnetic nature of Sample P and Sample Q. Give one identifying property of each. [1 mark]

(ii) For Sample P, the applied magnetic field intensity H = 1200 A/m and the intensity of magnetisation M = 2.4 × 10⁵ A/m. Calculate the relative permeability μᵣ of Sample P. [1 mark]

(iii) The geologist heats Sample P above a certain critical temperature and repeats the experiment. She finds that it no longer shows strong attraction; instead, it behaves like Sample P at room temperature had very weak alignment. Name this critical temperature and explain what happens to the internal structure of the material at this temperature. [1 mark]

(iv) A uniform external magnetic field B⃗ = 0.4 T is applied. Compare the magnetic field inside Sample P (χ = 200) with that inside Sample Q (χ = −0.00015). Which has a greater magnetic field inside it, and by approximately how much? [1 mark]

A geologist surveys a rocky terrain and observes unusual compass deflections near certain rock samples. By carefully studying the field-line patterns and magnetic response of the samples in controlled external fields, she classifies the samples into different magnetic categories. Her measurements reveal that one sample crowds the magnetic field lines slightly into itself, while another sample actually repels the field lines faintly. These contrasting behaviours form the basis for the questions below.

A geologist is surveying a region and notices that a compass needle placed near a rock sample gets slightly attracted towards the sample and the field lines around the sample appear to converge (crowd slightly) into it. She records the following observations:
(i) The sample weakly attracts both poles of a bar magnet.
(ii) When placed in an external magnetic field B⃗, the sample develops a weak magnetisation in the direction of B⃗.
(iii) The relative permeability μᵣ of the sample is slightly greater than 1.
(iv) On heating the sample strongly, its magnetic behaviour practically vanishes above a certain temperature.

Based on these observations, answer the following:
(a) Identify the magnetic class (type) of the material. Give ONE characteristic property that distinguishes it from diamagnetic materials. [1]
(b) The sample has a volume of 2×10⁻⁵ m³ and, when placed in an external field of 0.4 T, acquires a uniform magnetisation M = 3.2 A m⁻¹. Calculate the magnetic moment of the sample. [1]
(c) A small bar magnet of moment m = 0.5 A m² is placed at the centre of a circular coil of 50 turns, radius 0.2 m, carrying a current of 2 A, with its axis along the axis of the coil. Calculate the magnitude of the torque on the bar magnet if it is tilted so that its axis makes an angle of 30° with the magnetic field of the coil. [1]
(d) The geologist also finds a second sample whose magnetic susceptibility χ is small and negative. Identify its magnetic class and state whether its relative permeability μᵣ is greater than, equal to, or less than 1. [1]

A geophysicist studies two rock samples: Sample P (strongly attracted to a magnet, retains magnetisation) and Sample Q (weakly repelled, no retained magnetisation). Sample P has magnetic dipole moment M = 0.48 A m²; Earth's horizontal component B_H = 0.30 × 10⁻⁴ T; distance on equatorial line r = 0.20 m.

A geophysicist is analysing the magnetic properties of two rock samples collected from different geological sites. Sample P is found to be strongly attracted to a bar magnet and retains its magnetisation even after the magnet is removed. Sample Q is weakly repelled by the same bar magnet and loses any induced magnetisation the moment the external field is removed.

(i) Identify the magnetic class of Sample P and Sample Q. Give one distinguishing property of each.

(ii) Sample P, when analysed, is found to have a magnetic dipole moment M = 0.48 A m² and is placed with its axis along the direction of Earth's horizontal component of magnetic field B_H = 0.30 × 10⁻⁴ T. Calculate the torque acting on it when its axis makes an angle of 30° with B_H.

(iii) The geophysicist now places Sample P (treated as a small bar magnet of moment M = 0.48 A m²) at a point on the equatorial line at a distance r = 0.20 m from its centre. Calculate the magnitude of the magnetic field at that point.

(iv) If the temperature of Sample P is raised well above its Curie temperature, predict what happens to its magnetic behaviour. Justify your answer.

A geophysics student studies three volcanic rock samples X, Y, and Z placed in a strong external magnetic field. Sample X is feebly magnetised along the field and loses magnetism on removal. Sample Y is strongly magnetised along the field and retains magnetism on removal. Sample Z is feebly magnetised opposite to the field and loses magnetism on removal.

A geophysics student is studying the magnetic properties of three rock samples collected from different volcanic sites. She places each sample inside a strong external magnetic field and observes the following:

• Sample X: Gets feebly magnetised in the direction of the external field; loses magnetism completely when the field is removed.
• Sample Y: Gets strongly magnetised in the direction of the external field; retains a large amount of magnetism even after the field is removed.
• Sample Z: Gets feebly magnetised in the direction OPPOSITE to the external field; loses magnetism when the field is removed.

Based on these observations, answer the following questions:

(i) Identify the magnetic class (paramagnetic, diamagnetic, or ferromagnetic) of each sample X, Y, and Z.
(ii) The student measures the magnetic susceptibility (χ) of Sample X. State the sign and approximate magnitude (small/large) of χ for Sample X.
(iii) Sample Y is made into a toroid of mean radius 10 cm, wound with 500 turns, and a current of 2 A is passed through it. Given that the relative permeability μᵣ of Sample Y is 800, calculate the magnetic field B inside the toroid.
(iv) Explain briefly why Sample Z cannot be used as a permanent magnet.

A geologist on a field expedition uses a bar magnet (magnetic dipole moment M = 2.0 A m²) for navigation. She observes compass needle behaviour at various positions around the magnet. The equatorial line is the perpendicular bisector of the magnet's axis. (μ₀/4π = 10⁻⁷ T m A⁻¹)

A geologist on a field expedition carries a small compass needle and a bar magnet for navigation. She notices that when she places the bar magnet with its north pole pointing geographically north, the compass needle at a point on the equatorial line of the bar magnet (at a distance of 10 cm from its centre) deflects and aligns itself parallel to the bar magnet's axis. The bar magnet has a magnetic dipole moment of 2.0 A m².

(i) What is the direction of the magnetic field at a point on the equatorial line of a bar magnet?
(ii) Write the formula for the magnetic field on the equatorial line of a bar magnet and calculate its magnitude at a distance of 10 cm from its centre. (Use μ₀/4π = 10⁻⁷ T m A⁻¹)
(iii) If the geologist replaces the bar magnet with a circular current-carrying loop of radius 5 cm carrying a current of 2 A, what is the magnetic dipole moment of the loop?
(iv) Name the class of magnetic materials that the geologist's compass needle is most likely made of, and state ONE property that makes it suitable for this purpose.

Earth's magnetic field plays a crucial role in navigation and geophysical studies. A compass needle — essentially a magnetic dipole — aligns itself along the horizontal component of Earth's field (B_H). The oscillation of such a needle about equilibrium, when disturbed, provides a method to measure magnetic moments. Magnetic materials are classified based on their behaviour in an external field: diamagnetic, paramagnetic, and ferromagnetic. Every ferromagnetic material has a characteristic Curie temperature above which it loses its ferromagnetic property. The Earth's total field B_E is related to its horizontal component B_H and the angle of dip δ by: B_H = B_E cos δ.

A geophysics research team is studying the Earth's magnetic field at a remote location. They set up a small compass needle (a magnetic dipole of magnetic moment m = 0.12 A m²) at a point where the Earth's horizontal component of magnetic field is B_H = 3.6 × 10⁻⁵ T. The needle is displaced by a small angle from its equilibrium position and released.

(i) Name the type of magnetism exhibited by the material used in a permanent bar magnet. State ONE property that distinguishes it from paramagnetism.

(ii) When the compass needle oscillates about its equilibrium position, the time period of oscillation is given by T = 2π√(I/mB_H), where I is the moment of inertia of the needle. If the moment of inertia of this needle about its centre is I = 4.8 × 10⁻⁷ kg m², calculate the time period of oscillation.

(iii) The team heats the bar magnet to a temperature well above its Curie temperature. State and explain what happens to its magnetic properties.

(iv) At the same location, if the angle of dip is 60°, calculate the magnitude of the Earth's total magnetic field B_E at that location.

A bar magnet of magnetic dipole moment M = 0.5 A m² is placed horizontally on a table. A compass needle is used to explore the magnetic field at various points around the magnet. Point P lies on the axial line and point Q lies on the equatorial line, both at a distance r = 20 cm = 0.20 m from the centre of the magnet. (Use: μ₀/4π = 10⁻⁷ T m A⁻¹)

A bar magnet is placed on a table. A student observes that a compass needle placed at point P (on the axial line, 20 cm from the centre of the magnet) shows a deflection, and the needle aligns along the field of the magnet. The magnetic dipole moment of the bar magnet is 0.5 A m².

(i) Name the physical quantity that describes the strength of a magnetic dipole. Write its SI unit.
(ii) Calculate the magnitude of the magnetic field at point P on the axial line.
(iii) If the compass needle is now moved to point Q on the equatorial line at the same distance (20 cm) from the centre, how does the magnitude of the field at Q compare with that at P? Give the ratio B_axial : B_equatorial.
(iv) A student claims that the field lines of a bar magnet form closed loops, unlike electric field lines of a dipole which begin and end on charges. Is the student correct? Justify briefly.

The magnetic permeability of a ferromagnetic material is

Assertion (A) : A diamagnetic substance, when placed in a non-uniform magnetic field, moves from the stronger region to the weaker region of the field.
Reason (R) : The magnetic susceptibility of a diamagnetic material is small and negative.

A bar magnet of magnetic dipole moment M is placed along the x-axis. The ratio of the magnetic field at a point on its axial line to the magnetic field at a point on its equatorial line, both at the same distance r from the centre, is:

Assertion (A) : A paramagnetic substance is weakly attracted towards the stronger region of an external magnetic field.

Reason (R) : The magnetic susceptibility of a paramagnetic substance is small and negative.

A bar magnet is placed inside a solenoid and the solenoid is filled with a paramagnetic material. Which one of the following correctly describes the magnetic susceptibility (χ) of the paramagnetic material?

A bar magnet of magnetic moment 0.5 A m² is placed in a uniform magnetic field of strength 0.2 T such that its axis makes an angle of 30° with the field direction. Find (i) the torque acting on the magnet and (ii) the potential energy of the magnet in this position.

A bar magnet of magnetic moment 2.5 J T⁻¹ is placed with its axis along the direction of a uniform magnetic field of magnitude 0.4 T. Calculate the torque acting on the magnet and the potential energy of the magnet in this position.

A bar magnet of magnetic moment 2.5 A m² is placed with its axis along the direction of a uniform magnetic field of magnitude 0.4 T. Calculate: (a) the torque acting on the magnet, and (b) the potential energy of the magnet in this position.

A short bar magnet of magnetic moment m = 0.6 J T⁻¹ is placed with its axis making an angle of 60° with a uniform external magnetic field of magnitude B = 0.2 T. Calculate the torque acting on the magnet and state whether this torque tends to align or dis-align the magnet with the field.

A bar magnet of magnetic moment 0.6 J T⁻¹ is placed in a uniform external magnetic field of 0.4 T. (a) What is the work done in rotating the magnet from its equilibrium position (θ = 0°) to a position where it makes an angle of 60° with the field direction? (b) What is the torque on the magnet when it makes an angle of 30° with the field?

A research team is studying the magnetic behaviour of three unknown materials X, Y, and Z. They record the following observations:
• Material X: When placed in a non-uniform external magnetic field, it moves from the stronger region to the weaker region. Its susceptibility χ is a small negative constant, independent of temperature.
• Material Y: It shows a very strong attraction towards a magnetic field. When the external field is removed, it retains magnetisation. Its B–H curve forms a wide hysteresis loop.
• Material Z: Its susceptibility follows Curie's law χ = C/T, where C is the Curie constant and T is the absolute temperature. At temperature T_C it undergoes a phase transition.

(i) Identify the magnetic class (diamagnetic / paramagnetic / ferromagnetic) of each material X, Y, and Z. Give one distinguishing property for each. [1 mark]
(ii) The hysteresis loop of material Y has a large area. What does this imply about energy loss per cycle? State one practical application for which this property makes Y suitable. [1 mark]
(iii) Material Z is initially ferromagnetic and is heated above the temperature T_C mentioned above. Name the temperature T_C and explain, at the atomic level, why Z becomes paramagnetic above T_C. [1 mark]
(iv) A small sample of material X (volume 2 × 10⁻⁶ m³, χ = −8 × 10⁻⁶) is placed in a uniform magnetic field of intensity H = 10⁵ A m⁻¹. Calculate the magnetisation M of the sample and hence find the magnetic moment m of the sample. [1 mark]

A geologist on a field expedition carries a sensitive magnetometer to study magnetic anomalies in the Earth's crust. At a certain location, she places a small bar magnet of magnetic moment M = 0.60 A m² on a horizontal surface. She then measures the magnetic field at two points:

(i) Point P, situated on the axial line of the magnet at a distance of 20 cm from its centre.
(ii) Point Q, situated on the equatorial line of the same magnet at the same distance of 20 cm from its centre.

She also notices that when she places a small sample of the rock (collected from the site) near the magnet, the rock gets weakly repelled by both poles of the magnet.

(a) Calculate the magnetic field at point P (axial point). [1 mark]
(b) Calculate the magnetic field at point Q (equatorial point). [1 mark]
(c) Compare the directions of the magnetic fields at P and Q relative to the magnetic moment M of the bar magnet. [1 mark]
(d) Identify the magnetic nature of the rock sample. Give ONE characteristic property that justifies this identification. [1 mark]

A geophysics research team is surveying a region near an active volcanic zone. They use a sensitive magnetometer and record the following observations at three test sites:

• Site P: A cylindrical rock sample is found to strongly attract the magnetometer probe even when the external field is removed.
• Site Q: A mineral sample placed in a non-uniform external magnetic field B⃗ moves weakly toward the stronger field region. Its susceptibility χ is measured as +3.2 × 10⁻⁵.
• Site R: A crystal sample, when placed inside a solenoid, produces an internal field slightly less than the applied field B₀. Its relative permeability μᵣ = 0.99982.

The team also finds a uniformly magnetised cylindrical bar (from Site P) of length 12 cm and cross-sectional area 2.0 cm², with a magnetic moment of 1.44 A m².

(i) Identify the magnetic material class at each site (P, Q, R) and give one distinguishing property of each.
(ii) For the sample at Site Q, calculate the magnetisation M (intensity of magnetisation) if the applied field H = 8.0 × 10⁴ A m⁻¹.
(iii) Calculate the pole strength of the bar from Site P.
(iv) The bar from Site P is heated above its Curie temperature and then brought near a compass needle. Predict and justify the observation.

A geophysicist is analysing magnetic data from two different locations on Earth's surface. At Location P, the angle of dip is 30° and the horizontal component of Earth's magnetic field is measured as 4×10⁻⁵ T. At Location Q, the horizontal component is the same (4×10⁻⁵ T) but the vertical component is 4√3×10⁻⁵ T.

(i) Calculate the total magnetic field intensity (B) at Location P.
(ii) Calculate the angle of dip at Location Q.
(iii) A small compass needle (magnetic moment m = 0.06 A m²) is placed at Location P with its axis initially aligned along the total Earth's field. It is then rotated in the vertical plane until the torque on it equals half its maximum possible torque at that location. What is the angle of rotation from its initial position?
(iv) A sample of bismuth (a diamagnetic material) is brought near the north pole of a strong bar magnet at Location Q. Describe the nature of force experienced by the bismuth sample and explain the physical reason using the concept of magnetisation.

An electron of mass m and charge e revolves in a circular orbit of radius r around the nucleus of a hydrogen atom with speed v.
(a) Derive an expression for the magnetic moment (μ) associated with the orbital motion of the electron.
(b) Write the expression relating the magnetic moment vector (μ⃗) and the orbital angular momentum vector (L⃗) of the electron, and state the significance of the negative sign.
(c) A paramagnetic sample is placed in an external magnetic field. State what happens to its magnetisation when the external field is (i) increased at constant temperature, and (ii) temperature is raised at constant external field.

A geophysicist is studying two remote locations X and Y on Earth's surface. At location X, the observed dip angle is 0° and the horizontal component of Earth's magnetic field is measured as 4×10⁻⁵ T. At location Y, the dip angle is 60° and the horizontal component is 2×10⁻⁵ T.

(a) Identify the geographic location of X. Calculate the total (resultant) magnetic field at X. (1 mark)

(b) Calculate the total magnetic field at Y and determine the vertical component of Earth's field at Y. (2 marks)

(c) A small bar magnet of magnetic moment m = 0.4 A m² is placed at location Y, oriented so that its axis aligns with Earth's total field at Y. Calculate the torque experienced by this magnet when it is then rotated by 90° from this equilibrium position. (1 mark)

A geologist working in a remote field notices that her compass needle is behaving erratically near a large rock outcrop. On testing samples in a laboratory, two rock specimens are identified:
• Specimen P: When suspended freely near a strong magnet, it is weakly attracted and aligns along the field direction.
• Specimen Q: When brought near a magnet, it is weakly repelled and sets itself at right angles to the external field.
Based on this, answer the following questions:
(i) Identify the magnetic nature of Specimen P and Specimen Q.
(ii) Which specimen, P or Q, has a small positive value of magnetic susceptibility (χ)? Give one reason.
(iii) When Specimen P is placed in an external magnetic field, will the magnetic field lines inside the specimen be more concentrated or less concentrated than outside? Justify.
(iv) A third specimen R is strongly attracted to a magnet and retains its magnetism even after the magnet is removed. Name the type of magnetic material R belongs to. Give one example.

A bar magnet of magnetic dipole moment M is placed in a uniform external magnetic field B⃗. The axis of the magnet makes an angle of 60° with the direction of B⃗.

(a) Write the expression for the torque acting on the magnet.
(b) Calculate the torque if M = 2 A m², B = 0.5 T.
(c) In which orientation is the magnet in (i) stable equilibrium and (ii) unstable equilibrium? Give the value of torque in each case.

A geophysics research team is studying the magnetic properties of three rock samples collected from different geological sites. Sample P is strongly attracted to a bar magnet and retains its magnetisation even after the magnet is removed. Sample Q is weakly attracted to the bar magnet and loses its magnetisation as soon as the magnet is removed. Sample R is weakly repelled by both poles of the bar magnet.

(i) Identify the magnetic category (ferromagnetic / paramagnetic / diamagnetic) of each sample P, Q, and R.

(ii) The team places Sample Q in a non-uniform magnetic field. In which direction will it move — towards the stronger region or weaker region of the field? Justify using the sign of its susceptibility.

(iii) A bar magnet made from a material similar to Sample P has magnetic moment m = 2.4 A m² and is placed with its axis making an angle of 30° with a uniform external magnetic field B = 0.08 T. Calculate the torque acting on it.

(iv) The team observes that when Sample P is heated above a certain temperature, it starts behaving like Sample Q. Name this temperature and state what happens to the magnetic domains of Sample P at this temperature.

A geophysics research team is mapping the Earth's magnetic field at a remote location. They place a small compass needle (modelled as a magnetic dipole of magnetic moment m = 0.08 A m²) at a point where the Earth's horizontal component of magnetic field is B_H = 0.4 × 10⁻⁴ T and the angle of dip is 60°.

(i) Calculate the magnitude of the Earth's total magnetic field B_E at that location.

(ii) The compass needle is displaced by a small angle from its equilibrium position and released. If the moment of inertia of the needle about its pivot is I = 2 × 10⁻⁶ kg m², calculate the time period of its oscillation.

(iii) The team then carries the same compass to a place where the angle of dip is 90°. State what happens to the time period of oscillation at this new location, giving a physical reason.

(iv) At the original location, if the needle is held at 30° from the direction of B_H, find the restoring torque acting on it.

Distinguish between diamagnetic, paramagnetic, and ferromagnetic materials on the basis of (i) magnetic susceptibility and (ii) behaviour in a non-uniform magnetic field. Give one example of each.

A geophysics team is surveying a region and places a small bar magnet M of magnetic moment m = 0.50 A m² at the origin of the x–y plane, with its magnetic moment directed along the +x axis. A compass needle (treated as a tiny magnetic dipole of moment m′ = 0.10 A m²) is placed, one position at a time, at the two locations given below:

Position I : at point A(d, 0), i.e., on the axial line of M, with m′ pointing along the +x axis.
Position II : at point B(0, d), i.e., on the equatorial line of M, with m′ pointing along the +x axis.

Take d = 10 cm.

(a) Calculate the magnitude of the magnetic field produced by M at point A and at point B. (2 marks)
(b) Find the potential energy of the compass needle in each position and hence state in which position the system has lower potential energy. (1 mark)
(c) In which position is the compass needle in stable equilibrium, unstable equilibrium, or not in equilibrium at all? Justify briefly. (1 mark)