CUET UG Physics Booster Test 2- Fundamentals of Magnetism

Oersted's experiment demonstrated that a current-carrying conductor produces a magnetic field around it. When the Earth's magnetic field is ignored, the magnetic field produced by the straight wire dominates the compass needle's behavior. The magnetic field lines around a long straight conductor are concentric circles centered on the wire. Since a magnetic needle always aligns tangentially to the magnetic field lines, the needle becomes tangential to these imaginary circular paths. Increasing the current increases the magnetic field strength according to the Biot-Savart law and Ampere's observations, leading to greater needle deflection. However, Statement 3 is incorrect because the plane of the circular magnetic field lines is perpendicular, not parallel, to the wire. NCERT uses this observation to explain the geometry of magnetic field lines around current-carrying conductors.

Faraday introduced the revolutionary concept of fields as real physical entities filling space. Maxwell mathematically developed this idea and unified electricity and magnetism through Maxwell's equations. One of the most important consequences of his theory was that electromagnetic disturbances propagate through space with a finite speed rather than instantaneously. When Maxwell calculated this speed, he found it equal to the known speed of light. This led him to conclude that light itself is an electromagnetic wave. The theory therefore established a deep connection between electricity, magnetism and optics. NCERT highlights Maxwell's work as a major breakthrough that transformed the understanding of electromagnetic interactions and demonstrated that changes in fields require finite time to travel through space.

The Lorentz force equation combines electric and magnetic effects acting on a charged particle. The magnetic part of the force is given by q(v × B), where × denotes the vector cross product. A cross product always produces a vector perpendicular to both participating vectors. Therefore, the magnetic force is perpendicular to both the velocity of the particle and the magnetic field. If the charge is stationary, v = 0 and the magnetic force becomes zero. The magnitude and direction of the magnetic force depend on the particle's velocity, magnetic field strength and charge. For negative charges, the force direction is opposite to that obtained for positive charges. Thus, Statement C is incorrect because the magnetic force is never parallel to both velocity and magnetic field.

The principle of superposition states that the resultant magnetic field at any point is obtained by adding the magnetic fields produced individually by all sources. Since magnetic fields possess both magnitude and direction, they must be added vectorially rather than algebraically. Depending on their directions, individual magnetic fields may reinforce or oppose each other. This principle is extensively used while analyzing magnetic fields due to multiple current-carrying conductors, loops and combinations of magnetic sources. NCERT emphasizes that magnetic fields obey the same superposition principle as electric fields. Therefore, the net magnetic field is the vector sum of the contributions from all individual current-carrying segments.

The magnetic field produced by a long straight current-carrying conductor is directly proportional to the current flowing through it and inversely proportional to the distance from the wire. Mathematically, B ∝ I/r where I is the current and r is the distance from the conductor. Therefore, increasing the current increases the magnetic field strength, causing a larger torque on the magnetic needle and hence greater deflection. Similarly, bringing the needle closer to the wire reduces the distance and increases the magnetic field strength, again producing greater deflection. NCERT uses these observations to explain how magnetic field strength depends on both current and distance. Thus, increasing current and decreasing distance both increase the magnetic effect observed on the compass needle.

Iron filings provide a visual representation of magnetic field lines because each filing behaves like a tiny magnet and aligns itself along the local magnetic field direction. Around a straight current-carrying conductor, the magnetic field lines are concentric circles centered on the wire. These circles represent locations where the magnetic field has a constant radial distance from the conductor. Another important property of magnetic field lines is that they form continuous closed loops. Unlike electric field lines, magnetic field lines do not begin or end anywhere because isolated magnetic monopoles have not been observed. Statements 3 and 4 are incorrect because electric field lines originate from positive charges and terminate on negative charges, whereas magnetic field strength depends directly on the magnitude of current producing the field.

For a circular current loop of radius R carrying current I, the magnetic field at the center is obtained from the Biot-Savart law. Integrating the contribution of all current elements around the loop gives B = μ₀I/2R The direction of the field is determined by the right-hand thumb rule. Curling the fingers in the direction of current flow and pointing the thumb perpendicular to the plane gives the direction of the magnetic field at the center. For an anticlockwise current viewed from above, the thumb points along the positive z-axis. According to the dot-cross convention, a magnetic field directed out of the plane is represented by a dot. Therefore, both the magnitude and direction are correctly represented by Option A.

Consider a straight conductor carrying current along the positive y-axis. Applying the right-hand thumb rule, the magnetic field lines circle around the wire. On the right side of the conductor (+x direction), the magnetic field points into the plane of the paper, corresponding to the negative z-direction. This is represented by a cross (⊗). On the left side (-x direction), the magnetic field points out of the plane of the paper, corresponding to the positive z-direction and represented by a dot (•). Thus, the field on the right side matches the cross symbol, the field on the left side matches the dot symbol, and the vector direction on the right side corresponds to the negative z-axis. The dot symbol represents a field directed along the positive z-axis.

For a charged particle moving perpendicular to a magnetic field, the magnetic force acts as the centripetal force. qvB = mv²/r Therefore, r = mv/qB Substituting the given values: r = (9 × 10⁻³¹ × 3 × 10⁷) / (1.6 × 10⁻¹⁹ × 6 × 10⁻⁴) r = (27 × 10⁻²⁴) / (9.6 × 10⁻²³) r = 0.28125 m r ≈ 0.28 m Converting to centimeters: r ≈ 28 cm Thus, the radius of the circular path is approximately 28 cm.

To suspend the wire in mid-air, the upward magnetic force must balance the downward gravitational force. Weight of wire: W = mg = 0.2 × 9.8 = 1.96 N Magnetic force on a current-carrying conductor: F = BIL For equilibrium, BIL = mg Therefore, B = mg/IL Substituting values: B = (0.2 × 9.8)/(2 × 1.5) B = 1.96/3 B = 0.653 T ≈ 0.65 T Hence, a magnetic field of approximately 0.65 tesla is required to suspend the conductor.

Oersted's experiment established that a current-carrying conductor produces a magnetic field around it. He observed that a compass needle placed near a conducting wire deflected whenever electric current flowed through the wire. The needle aligned tangentially to the circular magnetic field lines centered on the wire. He also found that the magnetic effect became stronger when the current increased or when the compass was brought closer to the conductor. From these observations, Oersted concluded that moving charges or electric currents generate magnetic fields in the surrounding space. However, he did not demonstrate that static charges produce magnetic forces on a compass needle. Static charges create electric fields but not magnetic fields. Therefore, Option C is the incorrect statement.

Maxwell's electromagnetic theory unified electricity and magnetism and predicted the existence of electromagnetic waves traveling at the speed of light. Since the calculated speed matched the known speed of light, Maxwell concluded that light itself is an electromagnetic wave. This prediction was experimentally verified by Heinrich Hertz, who successfully generated and detected radio waves. Later, J.C. Bose and Guglielmo Marconi developed techniques for producing and transmitting radio waves over long distances, laying the foundation of wireless communication. These developments revolutionized communication technology and directly resulted from Maxwell's theoretical work. NCERT highlights this sequence as one of the most important achievements in the history of physics.

The Biot-Savart law and Coulomb's law exhibit several mathematical similarities. Both involve inverse-square dependence on distance from the source. However, Coulomb's law describes electric fields generated by electric charges, which are scalar sources. In contrast, the Biot-Savart law describes magnetic fields generated by current elements, which have directional properties and therefore behave as vector sources. Another important difference is that the Biot-Savart law contains a sinθ term, indicating angular dependence between the current element and the position vector. Coulomb's law does not contain such a term because the electric field due to a point charge is radially symmetric. Furthermore, μ₀ denotes permeability of free space and ε₀ denotes permittivity of free space. Hence all four statements are correct.

According to Maxwell's electromagnetic theory, c² = 1/(μ₀ε₀) Therefore, μ₀ε₀ = 1/c² Substituting c = 3 × 10⁸ m/s gives μ₀ε₀ = 1/(3 × 10⁸)² = 1/(9 × 10¹⁶) = (1/9) × 10⁻¹⁶ s²/m² Thus, the value of μ₀ε₀ is (1/9) × 10⁻¹⁶ s²/m². This relation is one of Maxwell's most important results because it links electric and magnetic constants with the speed of light, proving that light is electromagnetic in nature.

The magnetic field at the centre of a circular arc carrying current is B = μ₀Iθ/4πR For a semicircular arc, θ = π rad Therefore, B = μ₀I/4R Substituting the given values, B = (4π × 10⁻⁷ × 12)/(4 × 0.02) = (48π × 10⁻⁷)/0.08 = 600π × 10⁻⁷ ≈ 1.88 × 10⁻⁴ T ≈ 1.9 × 10⁻⁴ T Hence, the magnetic field at the centre of the semicircular arc is 1.9 × 10⁻⁴ T.

The SI unit of magnetic field is tesla (T), while gauss (G) is a CGS unit. The conversion factor is 1 G = 10⁻⁴ T Given, B = 6.5 G Therefore, B = 6.5 × 10⁻⁴ T This conversion is frequently used in magnetism because many practical magnetic field values are expressed in gauss while theoretical calculations use tesla. NCERT introduces both units and their conversion relation.

The twentieth century experienced unprecedented scientific and technological growth due largely to advances in electromagnetism. Maxwell's theory, Hertz's experiments and the development of radio communication by Bose and Marconi led to technologies such as radio, television, radar, satellite communication, mobile phones and the internet. Understanding electromagnetic waves enabled efficient transmission and reception of information over long distances. Electromagnetism also played a crucial role in electrical engineering, electronics, medical imaging and modern computing. NCERT emphasizes that developments in electromagnetic theory transformed both science and society.

Maxwell's theory predicts that electromagnetic disturbances propagate through space at a finite speed equal to the speed of light. These waves carry both energy and momentum, allowing information to be transmitted from one location to another. This property forms the basis of radio communication, television broadcasting, satellite communication and wireless networks. Electromagnetic waves do not act instantaneously across space; instead, changes in electric and magnetic fields propagate continuously. NCERT emphasizes that electromagnetic waves are self-sustaining oscillations of electric and magnetic fields capable of transporting energy through vacuum without requiring a material medium.

Ampere's circuital law states that the line integral of the magnetic field around any closed path equals μ₀ times the net current enclosed by that path. The law is mathematically expressed as ∮ B·dl = μ₀Ienc The closed path forms the boundary of an open surface through which current may pass. The law also supports the concept that magnetic field lines form continuous closed loops around currents. Ampere's law is especially useful in highly symmetric situations such as long straight conductors, solenoids and toroids, where the magnetic field can be easily determined. NCERT emphasizes these applications while deriving magnetic fields in symmetric configurations.

In electrostatics, the fundamental source of electric fields is the electric charge, which exists independently as positive or negative charges. Therefore, electric monopoles are the elementary building blocks of electrostatics. In contrast, isolated magnetic poles or magnetic monopoles have never been experimentally observed. Every magnet possesses both north and south poles. Consequently, the simplest magnetic entity is a magnetic dipole, which may be represented by a current loop. NCERT emphasizes this distinction when comparing electric and magnetic fields. Because magnetic monopoles are unknown in nature, magnetic dipoles become the fundamental building blocks of magnetism.