CUET UG Physics Booster Test 3- Fundamentals of Magnetism

Hans Christian Oersted observed that a compass needle placed near a current-carrying conductor gets deflected whenever current flows through the wire. This observation provided the first experimental evidence that electricity and magnetism are related phenomena. According to NCERT, the magnetic field produced by a straight current-carrying conductor consists of concentric circular field lines centered on the conductor. The direction of the magnetic field at any point is tangential to these circular field lines and can be determined using the right-hand thumb rule. Since the compass needle always aligns itself along the magnetic field direction, it becomes tangent to the circular magnetic field lines. Therefore, the needle is not parallel to the conductor. If the current direction is reversed, the magnetic field direction also reverses, causing the compass needle to deflect in the opposite direction. Iron filings reveal the pattern of magnetic field lines as concentric circles around the wire. Hence, statement B is incorrect and is the correct answer to the question.

Michael Faraday introduced the revolutionary concept of electric and magnetic fields. Before Faraday, interactions were generally explained using action-at-a-distance ideas. Faraday proposed that charges and magnets create fields in the surrounding space, and changes in these fields propagate through space. This idea laid the foundation for modern electromagnetic theory. James Clerk Maxwell later formulated a complete mathematical theory of electromagnetism using a set of equations now known as Maxwell's equations. These equations unified electricity and magnetism into a single framework and predicted the existence of electromagnetic waves. Maxwell showed that electromagnetic waves travel with a speed equal to the speed of light, leading to the conclusion that light itself is an electromagnetic wave. Thus, Faraday is credited with introducing the field concept and finite propagation ideas, while Maxwell provided the mathematical unification of electricity, magnetism and light. Therefore, option A is correct.

The magnetic force acting on a moving charged particle is given by the Lorentz force equation: F = q(v × B) The velocity is along the +x-direction. The force experienced by the electron is along the −z-direction. Since the electron carries a negative charge, the direction of force is opposite to the direction of the vector product (v × B). If B is along the +y-axis, then: î × ĵ = k̂ Thus, v × B points along +z. Because the particle is an electron, the force acts opposite to +z, which is −z. This matches the given condition exactly. The magnetic field cannot be along the z-axis because then the cross product would produce force along the y-direction. Therefore, only a magnetic field along the +y-axis satisfies the given information. Hence, option C is correct.

According to the Biot-Savart law, the magnetic field due to a current element is proportional to I dl sinθ. This expression is linear in the current element, which allows the principle of superposition to be applied. When several current elements contribute to the magnetic field at a point, the total magnetic field is obtained by vector addition of individual contributions. The angle dependence represented by sinθ remains part of each differential contribution and is considered throughout the integration process. Because magnetic fields obey superposition, the net field due to an extended conductor or current loop can be calculated by integrating dB over the entire current distribution. For example, the magnetic field at the center of a circular current loop is obtained by summing the contributions of all current elements around the loop. Therefore, all four statements correctly describe the role of superposition in the Biot-Savart law.

According to NCERT, the magnetic field produced by a straight current-carrying conductor consists of concentric circles centered on the conductor. The direction of these magnetic field lines can be determined using the right-hand thumb rule. A compass needle always aligns itself along the direction of the resultant magnetic field at its location. When the conductor is placed along the Earth's north-south direction and a compass is positioned directly above the wire, the magnetic field due to the conductor is tangential to the circular field lines. If the current is sufficiently large, the magnetic field produced by the wire becomes much stronger than the Earth's magnetic field. In such a situation, the compass responds mainly to the magnetic field of the wire rather than the Earth's field. At the point directly above the wire, the magnetic field is directed along the east-west direction. Therefore, the compass needle aligns tangentially to the circular magnetic field lines and becomes perpendicular to the wire. Hence, the needle points along the east-west direction, making Option B correct.

Iron filings are commonly used to visualize magnetic field patterns around magnets and current-carrying conductors. When sprinkled around a straight current-carrying wire, the filings arrange themselves along concentric circular paths, revealing the shape of the magnetic field lines. This demonstrates the cylindrical symmetry of the magnetic field around the conductor. However, iron filings only provide a qualitative representation of the magnetic field. They do not measure the magnitude of the field at different points. To determine the exact strength of the magnetic field, mathematical expressions such as the Biot–Savart law or Ampere's law must be used. Furthermore, iron filings alone cannot indicate the direction of the magnetic field. A magnetic compass is needed to identify the direction of the field at a particular point because the compass needle aligns tangentially to the field lines. Therefore, statements 2, 3 and 4 are correct, whereas statement 1 is incorrect.

The magnetic dipole moment of a current-carrying circular loop is given by: m = IA where I is the current and A is the area vector. The magnitude of the area vector for a circular loop is πR². The direction of the magnetic moment is determined using the right-hand thumb rule. If the fingers curl in the direction of current, the thumb points in the direction of the magnetic moment. A dot (·) represents a vector coming out of the plane of the paper. Since the loop lies in the xy-plane, the outward direction corresponds to the positive z-axis or k̂ direction. Therefore, the magnetic moment vector is: m = I(πR²)k̂

For a straight conductor carrying current along the positive x-axis, the magnetic field direction is determined using the right-hand thumb rule. At a point on the positive y-axis, the magnetic field points outward from the plane, represented by a dot. At a point on the negative y-axis, the field points inward, represented by a cross. For a circular loop, the right-hand thumb rule is again applied. If the current is clockwise when viewed from above, the magnetic field at the center is directed inward. If the current is anticlockwise, the magnetic field at the center is directed outward. Thus: 1 → a 2 → b 3 → c 4 → d Therefore, Option A gives the correct matching.

The magnetic force acting on a moving charged particle is given by: F = q(v × B) The force is always perpendicular to the instantaneous velocity of the particle. Since work done is given by: W = F · s and the force remains perpendicular to displacement, the scalar product becomes zero. Therefore, the magnetic force does no work on the particle. As a result, the kinetic energy of the particle remains constant. Since kinetic energy depends on speed, the magnitude of velocity remains unchanged. However, the direction of velocity may change continuously, causing the particle to move in circular or helical paths. This property is fundamental to the operation of cyclotrons, mass spectrometers and many charged particle devices. Hence Option D correctly describes the consequence of the magnetic force being perpendicular to velocity.

The magnetic field at the center of a circular coil having N turns is: B=μ_0NI/2R Given: N = 100 I = 1 A R = 10 cm = 0.1 m μ₀ = 4π × 10⁻⁷ T m A⁻¹ Substituting: B=(4π×10^(-7))(100)(1)/2(0.1)B=4π×10^(-5)/0.2B=20π×10^(-5)B=6.28×10^(-4)  T Unit Verification (T·m/A × A)/m = T Thus, the SI unit obtained is Tesla, confirming dimensional correctness. Therefore, the magnetic field at the center of the coil is 6.28 × 10⁻⁴ T.

In 1820, Hans Christian Oersted discovered that a compass needle placed near a current-carrying conductor undergoes deflection whenever electric current flows through the wire. Before this discovery, electricity and magnetism were considered entirely separate branches of physics. Oersted's experiment demonstrated that an electric current can produce a magnetic effect, thereby revealing a direct relationship between electrical and magnetic phenomena. This observation became one of the most important milestones in the development of electromagnetism. It provided the first empirical evidence that electricity and magnetism are interconnected. The discovery inspired scientists such as Ampere, Faraday and Maxwell to investigate electromagnetic interactions further. Ultimately, these studies led to Maxwell's electromagnetic theory, which unified electricity, magnetism and light. Therefore, the immediate and fundamental insight obtained from Oersted's experiment was that electricity and magnetism are closely related physical phenomena. Hence, Option B is correct.

Faraday introduced the concept of electric and magnetic fields as physical entities filling space. Maxwell extended this idea mathematically through his famous equations. One of Maxwell's most significant contributions was showing that electric and magnetic fields are dynamic quantities that can change with both position and time. According to Maxwell's equations, a changing electric field produces a magnetic field, and a changing magnetic field produces an electric field. This mutual generation allows electromagnetic disturbances to propagate through space in the form of electromagnetic waves. These waves travel at the speed of light and carry both energy and momentum. This theoretical framework led Maxwell to conclude that light itself is an electromagnetic wave. Therefore, electromagnetic fields are not merely static entities; they can evolve with time and transport energy across space. This insight forms the basis of modern electromagnetic theory and many technologies such as radio communication and optical transmission. Hence, Option C is correct.

A long solenoid consists of a large number of closely wound turns carrying current. Using Ampere's circuital law, ∮ B · dl = μ₀Ienclosed an Amperian rectangular path is chosen partly inside and partly outside the solenoid. For an ideal long solenoid, the magnetic field outside is nearly zero, while the field inside is uniform and parallel to the axis. If n represents the number of turns per unit length and I is the current through each turn, then the enclosed current for a length l is: Ienclosed = nlI Substituting into Ampere's law: Bl = μ₀nlI Therefore, B = μ₀nI This result shows that the magnetic field inside a long solenoid depends only on the current and the turn density. It is independent of the radius of the solenoid, making the field highly uniform and useful in electromagnetic devices. Hence, Option A is correct.

Maxwell's electromagnetic theory established the relation: c=1/√(μ_0ε_0) Rearranging, ε_0=1/μ_0c^2 Substituting: μ_0=4π×10^(-7)c=3×10^8 m/sε_0=1/(4π×10^(-7))(9×10^(16))ε_0=1/36π×10^9 Evaluating numerically, ε_0=8.85×10^(-12) C^2/Nm^2 Thus, Option A and Option C are simply two different representations of the same physical constant. Since both values are equivalent, Option D is the correct answer.

The SI unit of magnetic field strength is Tesla (T). From the Lorentz force equation, F=qvBsin⁡θ For perpendicular motion (θ=90^∘), B=F/qv If a charge of 1 C moving with a velocity of 1 m/s experiences a force of 1 N, then the magnetic field is defined as 1 Tesla. Therefore, statement 2 is correct. Using the unit expression, T=N/Cm/s=Ns/Cm Thus statement 3 is also correct. The dimensional formula becomes: [M T^(-2) A^(-1)] making statement 1 correct. However, Tesla is a comparatively large unit. In many laboratory measurements, smaller units such as millitesla or microtesla are frequently encountered. Therefore, statement 4 is incorrect. Hence, statements 1, 2 and 3 are correct.

The SI unit of magnetic field is Tesla (T), while Gauss (G) is a commonly used CGS unit. The relationship between these units is: 1 T=10^4 G Given: B=3.0×10^(-5) T Converting to Gauss: B=(3.0×10^(-5))×10^4B=3.0×10^(-1)B=0.3 G The horizontal component of the Earth's magnetic field is typically of the order of 10^(-5) T, which corresponds to a fraction of a Gauss. Therefore, the converted value is 0.3 G. Unit Verification T×10^4=G Thus, the unit conversion is dimensionally correct. Hence, Option A is the correct answer.

James Clerk Maxwell developed a mathematical theory of electromagnetism and predicted the existence of electromagnetic waves. His equations showed that oscillating electric and magnetic fields could propagate through space at the speed of light. From this result, Maxwell concluded that light itself is an electromagnetic wave. Several years later, Heinrich Hertz experimentally generated and detected electromagnetic waves, thereby confirming Maxwell's prediction. Hertz's experiments provided direct evidence for the existence of radio waves and validated Maxwell's electromagnetic theory. The subsequent work of scientists such as Jagadish Chandra Bose and Guglielmo Marconi helped develop practical applications of electromagnetic waves, especially in wireless communication. These developments revolutionized science, engineering and technology throughout the twentieth century. Therefore, the statement that Hertz theorized electromagnetic waves before Maxwell formulated his laws is historically incorrect. Maxwell's theoretical prediction came first, followed by Hertz's experimental verification.

Modern electromagnetic theory treats electric and magnetic fields as real physical entities capable of storing and transporting energy and momentum. Maxwell's equations show that time-varying electric fields produce magnetic fields and vice versa. This mutual interaction allows electromagnetic waves to travel through space. Electromagnetic waves are responsible for radio communication, television broadcasting, mobile communication and many other technologies. These waves carry energy and momentum from one location to another. Moving electric charges and electric currents are the primary sources of magnetic fields. Therefore, statement 4 is correct. Statement 2 is also correct because electric and magnetic fields can vary with time and propagate through space. Statement 1 is incorrect because electromagnetic fields are physical entities capable of carrying momentum. Statement 3 is incorrect because changes in electromagnetic fields propagate at a finite speed equal to the speed of light rather than instantaneously. Hence, only statements 2 and 4 are correct.

Ampere's circuital law and Gauss's law are powerful tools used in electromagnetism. Although both are based on symmetry considerations, they differ in the type of mathematical integration involved. Ampere's law is expressed as: ∮B⋅dl=μ_0I_(enc) This involves line integration of the magnetic field around a closed one-dimensional path called an Amperian loop. Gauss's law for electricity is expressed as: ∮E⋅dA=Q_(enc)/ε_0 This involves surface integration of the electric field over a closed two-dimensional surface known as a Gaussian surface. Thus, Ampere's law deals with boundary line integrals, whereas Gauss's law involves flux through a closed surface. This distinction is fundamental in electromagnetic field analysis and forms the basis of many NCERT derivations. Therefore, Option D is correct.

A current-carrying circular loop behaves like a magnetic dipole. At distances much larger than the size of the loop, the magnetic field resembles the field of an ideal magnetic dipole. For an electric dipole, the axial field is: E=2p_e/4πε_0x^3 A useful analogy exists between electric and magnetic dipoles. Replacing the electric dipole moment p_e with the magnetic dipole moment m, and replacing the electric constant term 1/ε_0 with the magnetic constant μ_0, the axial magnetic field becomes: B=μ_0/4π2m/x^3 or B=μ_02m/4πx^3 This expression is widely used for describing the field of a magnetic dipole at distant points along its axis. The inverse cube dependence indicates that the magnetic field decreases rapidly with increasing distance. Therefore, Option B is correct.