CUET UG Physics Booster Test 2-Bar Magnet Properties and Fundamentals

According to NCERT, magnetic phenomena are universal in nature and occur over a vast range of scales. Magnetic fields are present in atoms, molecules, planets, stars, and even distant galaxies. The Earth itself behaves like a giant magnet due to processes occurring deep within its interior. Geological evidence shows that Earth's magnetic field existed long before the appearance of human beings. The Earth's magnetism has been present for millions of years, whereas human evolution is comparatively recent in geological history. Therefore, the statement that human evolution predates Earth's magnetism is scientifically incorrect. NCERT introduces magnetism as a universal phenomenon that permeates nature at microscopic and astronomical scales. Hence, options A, C, and D correctly describe magnetic phenomena, while option B contradicts established scientific understanding.

The history of magnetism discussed in NCERT begins with observations of naturally occurring magnetic materials. Earth's magnetic field predates human evolution and therefore matches with "Predates human evolution." The region known as Magnesia became historically important because naturally magnetized iron ore was found there. Thus, Magnesia corresponds to the region associated with natural magnets. The approximate period around 600 BC is linked with early observations and discoveries of magnetic ore deposits. These findings contributed significantly to the understanding of magnetic phenomena. The discovery of magnetite eventually led to the development of the term "magnet," making magnetite discovery correspond to the historical origin of the word magnet. These historical associations help students understand the evolution of scientific knowledge from simple observations of natural magnets to modern electromagnetic theory.

The directive property of a magnet refers to its tendency to align itself in a definite direction when freely suspended. Due to the Earth's magnetic field, a freely suspended magnet comes to rest approximately along the geographic north-south direction. Hence Statement 1 is correct. The end of the magnet that points towards the geographic north is called the north pole, making Statement 2 correct. Earth's magnetic field exerts a torque on the suspended magnet, causing this alignment. Therefore, Earth behaves as a magnet and Statement 4 is also correct. Statement 3 is incorrect because a freely suspended magnet does not align east-west. The north-south alignment is one of the most important experimental observations that led to the understanding of Earth's magnetism.

When an iron nail is placed near a bar magnet, the magnetic field of the magnet induces magnetic poles in the nail. This process creates an induced magnetic moment in the nail, making Statement 2 correct. Since the field around a bar magnet is non-uniform, Statement 1 is also correct. A magnetic dipole placed in an external magnetic field experiences a torque that tends to align it with the field. In a non-uniform field, it also experiences a net force toward regions of stronger magnetic field. Consequently, Statement 3 is correct. Statement 4 is incorrect because the induced magnetization generally causes attraction between the nail and the magnet. The pole induced near the magnet is opposite in nature, producing an attractive interaction rather than a repulsive one.

Gauss's law for magnetism states that the net magnetic flux through any closed surface is always zero. This law is expressed mathematically as ∮B⋅dA=0 The physical reason behind this result is the absence of isolated magnetic poles or magnetic monopoles. Unlike electric charges, which can exist independently as positive or negative charges, magnetic poles always occur in pairs. Therefore, magnetic field lines never begin or end at a single point. Instead, they form continuous closed loops. Because the number of magnetic field lines entering a closed surface equals the number leaving it, the total magnetic flux through the surface is zero. This principle is one of the fundamental laws governing magnetic fields and highlights the dipolar nature of magnets.

According to NCERT, magnetic monopoles have never been observed in nature. Therefore, when a bar magnet is sliced transversely into two parts, each fragment continues to possess both a north pole and a south pole. Instead of producing isolated poles, the original magnet is divided into two smaller magnets. The resulting pieces generally have smaller dimensions and reduced magnetic strength compared to the original magnet. However, each fragment still exhibits all the essential properties of a magnet, including the ability to align in a magnetic field and attract magnetic materials. This behavior strongly supports the concept that magnetic poles always occur in pairs. The experiment also demonstrates the difference between electric charges and magnetic poles. While electric charges can exist independently, magnetic poles cannot be isolated. Hence, slicing a magnet transversely produces two smaller magnets with somewhat weaker magnetic properties.

Iron filings are commonly used to visualize magnetic field lines around a magnet. When sprinkled around a bar magnet, they arrange themselves along the direction of the magnetic field. The resulting pattern clearly shows two distinct regions where the field is strongest, namely the north and south poles. This field-line arrangement resembles the field pattern associated with an electric dipole consisting of equal and opposite charges. Although magnetic poles are not identical to electric charges, the overall field geometry exhibits strong similarities. The crowded field lines near the poles and curved paths between them indicate the dipole nature of the magnetic field. The demonstration does not prove the existence of magnetic monopoles. Instead, it reinforces the idea that magnets possess two poles. Therefore, the iron filing pattern suggests the existence of a magnetic dipole similar in appearance to an electric dipole field.

A compass needle behaves as a magnetic dipole having magnetic moment m. When placed in a magnetic field B, it experiences a torque that tends to align the dipole with the magnetic field direction. The magnetic potential energy of a dipole in a magnetic field is given by U=-m⋅B or U=-mBcos⁡θ where θ is the angle between the magnetic moment vector and the magnetic field. The negative sign indicates that the potential energy is minimum when the magnetic moment is parallel to the magnetic field. This corresponds to stable equilibrium. When the dipole is anti-parallel to the field, the potential energy becomes maximum and the equilibrium is unstable. Therefore, the correct expression for the magnetic potential energy is −m·B.

Magnetic field lines possess several unique properties described in NCERT. They always form continuous closed loops. Outside a magnet, the lines emerge from the north pole and enter the south pole, while inside the magnet they continue from south to north. Thus, Statement 1 is correct. Statement 2 is incorrect because magnetic field lines certainly exist inside a bar magnet. In fact, the continuity of magnetic field lines requires them to pass through the interior of the magnet. Statement 3 is correct because Gauss's law for magnetism states that the net magnetic flux through any closed surface is zero. This result follows from the absence of magnetic monopoles. Statement 4 is also correct because electrostatic field lines originate from positive charges and terminate on negative charges. Therefore, they cannot form closed loops in electrostatics. Hence, Statements 1, 3 and 4 are correct.

NCERT states that magnetic field lines are imaginary curves drawn such that the tangent at any point on the curve gives the direction of the magnetic field vector B at that point. This property allows physicists to determine the direction of the magnetic field throughout a region of space. A small compass needle placed on a magnetic field line aligns itself along the tangent to that field line. Therefore, the tangent provides direct information about the direction of the magnetic field. However, the tangent alone does not provide the exact magnitude of the field. The density of field lines is instead related to field strength. The tangent also does not represent the trajectory of a charged particle because the actual path of a charged particle depends on its velocity and the Lorentz force. Therefore, the tangent specifically represents the direction of the magnetic field vector B.

Magnetic field lines provide a visual representation of the magnetic field. The strength of a magnetic field at a point is indicated by the density of field lines. Where field lines are crowded together, the magnetic field is stronger, while regions with fewer field lines correspond to weaker magnetic fields. A uniform magnetic field is represented by straight, parallel and equally spaced field lines because both the magnitude and direction remain constant throughout the region. On the other hand, unevenly spaced field lines indicate that the magnitude of the magnetic field changes from point to point, producing a non-uniform magnetic field. Therefore, high concentration corresponds to strong magnetic field, low concentration corresponds to weak magnetic field, parallel equally spaced lines correspond to a uniform magnetic field, and uneven spacing corresponds to a non-uniform magnetic field.

The direction of the magnetic field at any point is given by the tangent drawn to the magnetic field line at that point. If two magnetic field lines intersected, two different tangents could be drawn at the same point. This would imply two different directions for the magnetic field at that location, which is physically impossible. Since the magnetic field must have a unique direction at every point in space, magnetic field lines cannot intersect. Therefore, the correct conclusion is that the field direction would not remain unique if intersections occurred.

Electrostatic field lines originate from positive charges and terminate on negative charges. Since they begin and end on charges, they cannot form continuous closed loops. In contrast, magnetic field lines always form closed curves because isolated magnetic monopoles have not been observed. Magnetic field lines emerge from the north pole, enter the south pole externally, and continue through the magnet internally, forming complete loops. Therefore, the statement claiming that electrostatic field lines form closed loops is incorrect.

The magnetic force acting on a moving charge is given by F=q(v×B) This force is perpendicular to both the velocity and the magnetic field. Consequently, the magnetic force does not generally act along the magnetic field line. Therefore, calling magnetic field lines "lines of force" may lead to the misconception that force acts along the field line. To avoid this confusion, the term "magnetic field lines" is preferred in modern physics.

A long current-carrying solenoid produces a magnetic field pattern very similar to that of a bar magnet. At large distances, both behave as magnetic dipoles and generate comparable field distributions. If a bar magnet is cut into two pieces, each piece becomes a smaller magnet with its own north and south poles. Similarly, cutting a solenoid produces two smaller solenoid-like magnetic systems. An equivalent solenoid can be assigned the same magnetic moment as a bar magnet if both produce identical magnetic effects. A compass placed near either object responds similarly because the field geometry is nearly identical. Therefore, Statements 1, 2 and 3 are correct.

Ampere proposed that magnetic phenomena arise from microscopic circulating currents within matter. According to this hypothesis, a bar magnet can be visualized as consisting of a large number of tiny current loops whose magnetic effects add together. A current-carrying loop behaves as a magnetic dipole and possesses a magnetic moment. A solenoid itself is made up of many circular current loops and therefore certainly contains circulating currents. Hence Statements 1, 3 and 4 are correct, while Statement 2 is incorrect.

The magnetic moment of a current-carrying solenoid is m=NIA Given, N=800I=3.0AA=2.5×10^(-4)m^2 Substituting, m=800×3.0×2.5×10^(-4)m=2400×2.5×10^(-4)m=0.60 A m^2 Since 1 A m^2=1 J T^(-1)m=0.60 J T^(-1) Therefore, the associated magnetic moment is 0.60 J T^(-1).

For a short bar magnet treated as a magnetic dipole: Axial field, B_(axial)=μ_0/4π2m/r^3 Equatorial field, B_(equatorial)=μ_0/4πm/r^3 Taking the ratio, B_(equatorial)/B_(axial)=μ_0/4πm/r^3/μ_0/4π2m/r^3=1/2 Thus, the equatorial field is half the axial field at the same distance.

When a bar magnet is cut into two parts, each part behaves as an independent magnet. The magnetic domains within each piece remain aligned, causing each fragment to develop its own north and south poles. Thus, instead of obtaining isolated poles, two smaller complete magnets are produced. This observation supports the idea that magnetic poles always occur in pairs. Experimental attempts have never isolated a north pole or south pole by cutting a magnet. Therefore, each piece becomes a smaller dipole magnet with both poles present.

The poles of a bar magnet are concentrated near its ends, while the middle portion is nearly neutral. If one end of bar A is brought near the middle of bar B and no attraction is observed, then the middle of B behaves like the neutral region of a magnet. This indicates that B is the magnet and A is the ordinary iron bar. If B were merely an iron bar, the end of the magnet would induce magnetism in B and attraction would occur. Thus, the absence of force when testing the middle region identifies B as the magnet.