CUET UG Physics Booster Test 3-Bar Magnet Properties and Fundamentals

NCERT introduces magnetism as a universal phenomenon present throughout nature. Magnetic fields are not restricted to laboratory magnets but are observed in atoms, molecules, planets, stars, and even distant galaxies. Astronomical observations reveal that galaxies are permeated by large-scale magnetic fields, making Statement 1 correct. Atoms also possess magnetic properties because electrons have orbital motion and intrinsic spin, both of which produce magnetic moments. Therefore, Statement 2 is correct. Living organisms, including humans and animals, are composed of atoms and charged particles, so magnetic effects are present at microscopic levels, making Statement 4 correct. Statement 3 is incorrect because Earth's magnetic field existed millions of years before the appearance of human beings. Geological evidence clearly shows that Earth's magnetism predates human evolution. Hence, Statements 1, 2 and 4 are correct.

According to NCERT, the word "magnet" is believed to have originated from Magnesia, a region associated with naturally occurring magnetic ore called magnetite. Historical records indicate that the magnetic properties of this mineral were known around 600 BC. These early observations laid the foundation for the study of magnetism. Long before the discoveries of Oersted, Ampere, Biot, and Savart, people had already observed the attractive properties of magnetite. The ability of naturally magnetized stones to attract iron objects fascinated ancient civilizations and eventually led to the development of navigational compasses. Modern magnetic materials such as Alnico were developed much later and have no connection with the historical origin of magnetism. Therefore, the statement connecting magnetism with Magnesia around 600 BC correctly describes its historical origin.

A magnetic dipole placed in a uniform magnetic field experiences a torque given by τ=m×B This torque tends to align the magnetic dipole with the external magnetic field. Therefore, a freely suspended magnet rotates until it points approximately along the north-south direction, making Option A correct. In a uniform magnetic field, equal and opposite magnetic forces act on the two poles of the dipole. These forces produce torque but cancel each other in magnitude, resulting in zero net force. Therefore, Option D is correct. Since a magnetized needle experiences torque but not a net translational force in a uniform magnetic field, the statement claiming that it experiences a net force is incorrect. Hence, Option C is the required answer.

When an iron nail is brought near a bar magnet, the magnetic field of the magnet induces magnetization in the nail. This creates an induced magnetic moment within the iron nail, making Statement 2 correct. The magnetic field around a bar magnet is non-uniform, so Statement 1 is also correct. Because of induction, the end of the nail closest to the magnet acquires a pole opposite to the nearby pole of the magnet. Since unlike poles attract, the attraction on the nearer end is stronger than any repulsion on the farther end. Therefore, the net force is attractive, making Statement 3 correct. Statement 4 is incorrect because a magnetized object can experience both force and torque depending on its orientation relative to the field. Thus, Statements 1, 2 and 3 are correct.

Gauss's law for magnetism in its present form is ∮B⋅dS=0 This equation reflects the experimentally verified fact that isolated magnetic poles, known as magnetic monopoles, have never been observed. As a result, magnetic field lines always form closed loops. However, if magnetic monopoles were discovered, the law would require modification in the same way that Gauss's law for electricity relates electric flux to enclosed electric charge. In such a hypothetical situation, the net magnetic flux through a closed surface would be proportional to the enclosed magnetic charge q_m. The modified equation would be ∮B⋅dS=μ_0q_m where μ₀ is the permeability of free space. This expression represents the magnetic analogue of Gauss's law for electric fields. Therefore, Option B is correct.

According to NCERT, magnetic monopoles have not been experimentally observed. Whenever a bar magnet is broken into pieces, each fragment behaves as a complete magnet possessing both a north pole and a south pole. This behavior is fundamentally different from electric charges, which can exist independently as positive or negative charges. The inability to isolate a single north pole or south pole is one of the most important characteristics of magnetism. Even repeated cutting of a magnet fails to produce isolated poles. Instead, each piece becomes a smaller magnetic dipole. This observation is consistent with Gauss's law for magnetism, which states that the net magnetic flux through any closed surface is zero. Therefore, unlike electric charges, isolated magnetic poles do not exist, making Option A correct.

Magnetic field lines possess a definite direction. Outside a bar magnet, they emerge from the north pole and enter the south pole. Therefore, field lines outside a bar magnet correspond to "Directed from North to South pole." To maintain continuity, magnetic field lines continue inside the magnet from south pole to north pole. Thus, field lines inside a bar magnet correspond to "Directed from South to North pole." In a toroid, the magnetic field is almost entirely confined within the toroidal core due to the circular arrangement of turns. Therefore, the field lines of a toroid correspond to "Completely confined within the core." Since magnetic field lines never begin or end, they always form continuous closed loops. Therefore, the correct matching is 1-c, 2-a, 3-b, 4-d.

A small magnetic compass needle behaves as a magnetic dipole. When placed in a magnetic field, it experiences a torque and aligns itself along the direction of the magnetic field. Therefore, the orientation of the compass needle provides information about the direction of the magnetic field at a particular point. By moving the compass to different locations around a magnet and noting its orientation, one can map the magnetic field lines throughout space. This method is frequently described in NCERT for visualizing magnetic fields experimentally. Electric charges do not directly indicate magnetic field direction, and magnetic monopoles have never been observed. Therefore, compass needles remain one of the simplest and most effective tools for mapping magnetic field directions.

According to Ampere's circuital law, magnetic fields are generated by electric currents. Whenever magnetic field lines form closed circular paths, they are associated with regions through which current flows. For example, magnetic field lines surrounding a straight current-carrying conductor form concentric circles enclosing the conductor. In completely empty space where no current exists, such closed magnetic loops cannot arise independently. Magnetic field lines always originate from magnetic sources such as currents or magnetic dipoles. The statement does not imply the existence of magnetic monopoles. Instead, it emphasizes the intimate relationship between magnetic fields and electric currents. Therefore, a closed loop of static magnetic field lines must enclose a region through which current passes.

NCERT states that the tangent drawn at any point on a magnetic field line gives the direction of the magnetic field vector B at that point. This property is one of the most important characteristics of magnetic field lines and is used extensively in visualizing magnetic fields. When a small compass needle is placed on a magnetic field line, it aligns itself along the tangent to the field line. Thus, the tangent directly indicates the direction of the magnetic field. However, the tangent does not specify the magnitude of the field. The strength of the magnetic field is instead inferred from the density of field lines. Field lines never intersect because intersection would imply two different directions for the magnetic field at the same point, which is impossible. Therefore, the tangent represents only the direction of the magnetic field vector.

Magnetic field lines are used to represent both the direction and magnitude of a magnetic field. A region containing a larger number of field lines per unit area corresponds to a stronger magnetic field. Therefore, Statement A is correct. For a finite solenoid, magnetic field lines emerge from one end, curve through the surrounding space and re-enter at the opposite end, forming continuous closed loops. Hence Statement B is also correct. Magnetic flux through any closed surface is zero according to Gauss's law for magnetism because magnetic monopoles do not exist. Therefore, Statement D is correct. Statement C is incorrect because real magnetic fields always exhibit fringing near the edges of pole pieces. Although the field may be approximately uniform in the central region between pole faces, perfectly straight field lines without any fringing are never achieved in practice.

A magnetic field at any point in space possesses a unique direction. Magnetic field lines are drawn so that the tangent at any point gives the direction of the magnetic field. If two field lines were to intersect, there would be two possible tangents and therefore two possible field directions at the same point. Such a situation is physically impossible. The same reasoning applies to electrostatic field lines. Electric field intensity also possesses a unique direction at every point. Consequently, electrostatic field lines can never intersect. Statement 4 is incorrect because field lines inside a solenoid remain nearly parallel and do not intersect. Intersections would violate the uniqueness of the magnetic field direction. Therefore, Statements 1, 2 and 3 are correct.

The magnetic field of a short magnetic dipole and the electric field of a short electric dipole possess analogous mathematical forms. The equatorial magnetic field is given by: Bₑ = −μ₀m/4πr³ while the axial electric field of a short electric dipole is: Eₐ = 2p/4πε₀r³ The potential energies of dipoles in external fields are similarly expressed as: U = −m·B for magnetic dipoles and U = −p·E for electric dipoles. Statement 4 is incorrect because isolated electric charges exist naturally, whereas isolated magnetic poles have never been observed experimentally. Magnetic dipoles always occur as north-south pole pairs. Thus Statements 1, 2 and 3 are correct.

Electric field lines are defined so that their direction at any point gives the direction of the force on a positive test charge placed at rest. Magnetic field lines, however, indicate the direction of the magnetic field vector B and not necessarily the direction of force on a moving charged particle. The magnetic force on a charge is given by: F = q(v × B) Since the force depends on both velocity and magnetic field direction, knowing only the magnetic field line direction is insufficient to determine the force direction. Magnetic field lines also form continuous closed loops and do not begin or end at isolated magnetic charges. Therefore, Option B correctly describes an important distinction between magnetic and electric field lines.

For a short magnetic dipole at distances much greater than its length (r >> l), the axial magnetic field is given by: Baxial = μ₀(2m)/4πr³ Hence Item 1 matches with b. The equatorial magnetic field is: Bequatorial = −μ₀m/4πr³ The negative sign indicates that the field direction is opposite to the magnetic moment. Therefore Item 2 matches with c. When a magnetic dipole is placed in a uniform magnetic field, it experiences a torque: τ = m × B Thus Item 3 matches with a. The potential energy of a magnetic dipole in a magnetic field is: U = −m·B Hence Item 4 matches with d. Therefore the correct matching is 1-b, 2-c, 3-a and 4-d.

Ampere proposed that magnetic phenomena originate from circulating electric currents. Modern atomic theory supports this idea because electron orbital motion and electron spin produce microscopic current loops that generate magnetic moments. A current loop behaves as a magnetic dipole and produces a magnetic field similar to that of a bar magnet. Furthermore, a system may possess zero net charge and still exhibit a magnetic moment because magnetic properties depend on moving charges rather than net charge. Statement C is incorrect because Ampere's hypothesis explains magnetism in terms of circulating currents rather than requiring the existence of actual north and south magnetic charges. Magnetic poles are convenient descriptive concepts, not fundamental isolated entities. Therefore, magnetic behavior can be understood entirely through current distributions.

The torque experienced by a magnetic dipole in a uniform magnetic field is given by: τ = mB sinθ Given: τ = 4.5 × 10⁻² N m B = 0.25 T θ = 30° Since: sin 30° = 1/2 Substituting: 4.5 × 10⁻² = m × 0.25 × 0.5 4.5 × 10⁻² = 0.125m Therefore, m = (4.5 × 10⁻²)/0.125 m = 0.36 J T⁻¹ Thus the magnetic moment of the bar magnet is 0.36 J T⁻¹. The unit J T⁻¹ is equivalent to A m², which is the SI unit of magnetic dipole moment. Unit Verification m = τ/B = (N m)/T = J T⁻¹

A magnetic dipole placed in a uniform magnetic field experiences a restoring torque: τ = mB sinθ To rotate the dipole through an angle dθ against this torque, external work must be done. The change in potential energy is therefore related to the work performed against the restoring torque. Thus, U = −∫τ dθ Substituting the torque expression: U = −∫mB sinθ dθ U = −mB cosθ Since: m·B = mB cosθ the potential energy becomes: U = −m·B This expression shows that the potential energy is minimum when the magnetic moment is parallel to the magnetic field and maximum when antiparallel. Therefore, Option A correctly represents the derivation and final expression.

A magnetic needle behaves as a magnetic dipole. When placed in a uniform magnetic field, equal and opposite forces act on its poles. These forces cancel, producing zero net force. However, they form a couple that exerts a torque on the needle. The torque is given by: τ = mB sinθ where m is the magnetic moment and θ is the angle between m and B. This torque tends to align the magnetic moment with the external field. The potential energy of the dipole is: U = −mB cosθ This energy is minimum when θ = 0° and maximum when θ = 180°. Consequently, stable equilibrium occurs when the magnetic moment is parallel to the field. Thus, Option B correctly describes the restoring torque acting on a magnetised needle.

A standard method for identifying a magnet among two identical bars uses the fact that magnetic poles are concentrated at the ends of a magnet, whereas the central region is nearly neutral. If one end of bar A is brought near the middle of bar B and no significant force is observed, this indicates that the middle portion of B is magnetically neutral. Such behavior is characteristic of a magnet because its poles are localized at the ends. An unmagnetized iron bar, however, experiences induced magnetization when brought near a magnet and is attracted even at its middle region. Therefore, attraction at the center suggests the bar may simply be iron, whereas the absence of force at the middle indicates that the tested bar itself is magnetized. Hence, no force at the middle of B indicates that B is the magnetized bar.