CUET UG Physics Booster Test 3-Dipole Dynamics and Electrostatic Analogs -

🚀

CUET UG Physics Booster Test 3-Dipole Dynamics and Electrostatic Analogs

⏱️ 30 Minutes

❓ 20 Questions

📌 Answers are locked once submitted — results and explanations appear at the end.

CUET UG Physics Booster Test 3-Dipole Dynamics and Electrostatic Analogs

1 / 20

QUESTION 1 OF 20

Identify the correct statements regarding the vector product dynamics of a magnetic dipole in a uniform magnetic field.
Statements:
1. The magnitude of torque is maximized when the dipole is perpendicular to the field.
2. The vector product m × B ensures the torque is perpendicular to both m and B.
3. The restoring torque drives the dipole toward the θ = 180° position.
4. If the uniform field B increases, the maximum possible torque increases proportionally.

Answer Review

1 Identify the correct statements regarding the vector product dynamics of a magnetic dipole in a uniform magnetic field.
Statements:
1. The magnitude of torque is maximized when the dipole is perpendicular to the field.
2. The vector product m × B ensures the torque is perpendicular to both m and B.
3. The restoring torque drives the dipole toward the θ = 180° position.
4. If the uniform field B increases, the maximum possible torque increases proportionally.

A 1, 2 and 4 are correct

B 1, 3 and 4 are correct

C 2, 3 and 4 are correct

D 1, 2 and 3 are correct

💡 Short Explanation

�� Torque on a magnetic dipole is τ = mB sinθ. �� Maximum torque occurs at θ = 90°. �� Torque is perpendicular to both m and B.

✅ Correct Answer Explanation

A magnetic dipole placed in a uniform magnetic field experiences a torque given by τ = m × B and its magnitude is τ = mB sinθ where θ is the angle between the magnetic moment and the magnetic field. Since sin90° = 1, the torque becomes maximum when the dipole is perpendicular to the magnetic field. The cross-product nature of the equation ensures that the torque vector is perpendicular to both the magnetic moment and the magnetic field. The purpose of this torque is to rotate the dipole toward the stable equilibrium position where the magnetic moment becomes parallel to the magnetic field (θ = 0°), not toward θ = 180°. Since the maximum torque is proportional to both m and B, increasing the magnetic field strength increases the maximum torque proportionally.

❓ Why Other Options Are Incorrect

�� Option B → Statement 3 is incorrect because stable equilibrium occurs at θ = 0°.
�� Option C → Statement 3 is incorrect.
�� Option D → Statement 3 is incorrect.

🎯 Strategy

Used – Concept Application

Application
Use τ = mB sinθ and analyze the angular dependence of torque.
Final Logic
Statements 1, 2 and 4 follow directly from the torque equation, while Statement 3 is false.

🧠 Memory Trick

"Perpendicular Gives Peak Torque."

📚 Class: XII | Book: NCERT Physics Part I | Chapter: Magnetism and Matter | Topic: Torque in Uniform Fields | Subtopic: Torque on a Magnetic Dipole

2 A bar magnet of magnetic moment 1.5 J T⁻¹ lies aligned with the direction of a uniform magnetic field of 0.22 T. What is the amount of work required by an external torque to turn the magnet so as to align its magnetic moment opposite to the field direction?

A 0.33 J

B 0.66 J

C 0 J

D -0.66 J

💡 Short Explanation

�� Use magnetic potential energy. �� Initial angle θ = 0°. �� Final angle θ = 180°.

✅ Correct Answer Explanation

The potential energy of a magnetic dipole in a uniform magnetic field is U = -mB cosθ Initially, the dipole is aligned with the field: θ₁ = 0° Therefore, U₁ = -mB = -(1.5)(0.22) = -0.33 J Finally, the dipole is opposite to the field: θ₂ = 180° Therefore, U₂ = +mB = +(1.5)(0.22) = +0.33 J The work done by the external torque equals the increase in potential energy: W = U₂ - U₁ = 0.33 - (-0.33) = 0.66 J Thus, the required work is 0.66 J.

❓ Why Other Options Are Incorrect

�� Option A → Represents only mB, not the total energy change.
�� Option C → The potential energy changes significantly.
�� Option D → External work is positive because energy increases.

🎯 Strategy

Used – Formula Application

Application
Apply U = -mB cosθ for initial and final orientations.
Final Logic
Work required equals the increase in magnetic potential energy, which is 0.66 J.

🧠 Memory Trick

"Flip the Magnet → Energy Changes by 2mB."

📚 Class: XII | Book: NCERT Physics Part I | Chapter: Magnetism and Matter | Topic: Torque in Uniform Fields | Subtopic: Work Done in Rotating a Magnetic Dipole

3 Incorrect step in the conceptual derivation of magnetic potential energy.

A The restoring torque is mathematically expressed as τ = mB sinθ.

B The work done by an external torque is stored as potential energy.

C Setting the zero of potential energy at θ = 90° eliminates the arbitrary integration constant.

D The integration evaluates to +mB cosθ, defining the negative scalar product.

💡 Short Explanation

�� Potential energy is derived from torque. �� Integration introduces a constant. �� The correct expression is U = -mB cosθ.

✅ Correct Answer Explanation

The torque acting on a magnetic dipole is τ = mB sinθ To rotate the dipole slowly, an external torque equal and opposite to the magnetic torque is applied. The work done by this external torque is stored as magnetic potential energy. Therefore, dU = mB sinθ dθ Integrating, U = -mB cosθ + C where C is the integration constant. By choosing the reference level of potential energy to be zero at θ = 90°, the constant becomes zero. The resulting expression is U = -mB cosθ = -m·B Thus, the integration does not give +mB cosθ. The negative sign is essential because the energy must be minimum when the dipole aligns with the magnetic field.

❓ Why Other Options Are Incorrect

�� Option A → Correct expression for magnetic torque.
�� Option B → Correct interpretation of external work.
�� Option C → Correct method for choosing the reference energy.

🎯 Strategy

Used – Derivation Analysis

Application
Follow the integration process used to derive magnetic potential energy.
Final Logic
The correct integral yields -mB cosθ, not +mB cosθ.

🧠 Memory Trick

"Energy Minus, Torque Plus."

📚 Class: XII | Book: NCERT Physics Part I | Chapter: Magnetism and Matter | Topic: Potential Energy of Dipoles | Subtopic: Derivation of Magnetic Potential Energy

4 The scalar product representation of potential energy (-m·B) specifically establishes that

A the maximum potential energy occurs when the dipole is orthogonal to the magnetic field

B the energy of the dipole depends entirely on the cross product of the internal charges

C the potential energy is most negative when the dipole perfectly aligns with the uniform field

D the total energy of the system remains perfectly conserved only at 90 degrees

💡 Short Explanation

�� U = -mB cosθ. �� Minimum energy occurs at θ = 0°. �� Stable equilibrium corresponds to minimum energy.

✅ Correct Answer Explanation

The magnetic potential energy of a dipole in a uniform magnetic field is U = -m·B = -mB cosθ When the magnetic moment is aligned with the magnetic field (θ = 0°), U = -mB which is the minimum possible value. This corresponds to stable equilibrium. When the dipole is opposite to the field (θ = 180°), U = +mB which is the maximum possible value and corresponds to unstable equilibrium. At θ = 90°, the potential energy is zero. The scalar product form therefore directly shows that the most stable configuration occurs when the dipole moment and magnetic field are parallel.

❓ Why Other Options Are Incorrect

�� Option A → At θ = 90°, potential energy is zero, not maximum.
�� Option B → Potential energy depends on the scalar product m·B.
�� Option D → Conservation of energy is not restricted to θ = 90°.

🎯 Strategy

Used – Concept Application

Application
Analyze the expression U = -mB cosθ for different angular positions.
Final Logic
The most negative energy occurs when θ = 0°, meaning perfect alignment.

🧠 Memory Trick

"Aligned Means Lowest Energy."

📚 Class: XII | Book: NCERT Physics Part I | Chapter: Magnetism and Matter | Topic: Potential Energy of Dipoles | Subtopic: Magnetic Potential Energy

5 Regarding the conditions for stable equilibrium of a magnetic dipole

A It requires the magnetic moment to be orthogonal to the local magnetic field.

B It occurs exactly when the potential energy function reaches zero.

C It is achieved when the dipole aligns parallel to the external magnetic field, minimizing potential energy.

D It implies that the restoring torque is at its maximum possible theoretical value.

💡 Short Explanation

�� Stable equilibrium corresponds to minimum potential energy. �� The magnetic moment becomes parallel to the field. �� Torque becomes zero at equilibrium.

✅ Correct Answer Explanation

A magnetic dipole in a uniform magnetic field experiences a torque that tends to align its magnetic moment with the field. The magnetic potential energy is U = -mB cosθ The minimum value of U occurs when θ = 0°, meaning the magnetic moment is parallel to the magnetic field. This configuration corresponds to stable equilibrium because any small angular displacement increases the potential energy and produces a restoring torque that brings the dipole back to its equilibrium position. At equilibrium, the torque itself is zero because sin0° = 0. Thus, stable equilibrium is determined by minimum potential energy rather than maximum torque.

❓ Why Other Options Are Incorrect

�� Option A → Orthogonal orientation gives U = 0, not minimum energy.
�� Option B → Zero energy does not necessarily imply stability.
�� Option D → Torque is zero at stable equilibrium, not maximum.

🎯 Strategy

Used – Concept Application

Application
Use the relationship between potential energy, torque and equilibrium.
Final Logic
Stable equilibrium occurs when U is minimum and the dipole is parallel to the field.

🧠 Memory Trick

"Parallel is Peaceful."

📚 Class: XII | Book: NCERT Physics Part I | Chapter: Magnetism and Matter | Topic: Stability and Equilibrium | Subtopic: Stable Equilibrium of a Magnetic Dipole

6 Match List I (Energy Values) with List II (Equilibrium Characteristics).

List I	List II
1. U = −mB	a. Arbitrary non-equilibrium state, θ = 120°
2. U = +mB	b. Most stable position, θ = 0°
3. U = 0	c. Most unstable position, θ = 180°
4. U = mB/2	d. Neither maximum nor minimum, θ = 90°

A 1-b, 2-c, 3-d, 4-a

B 1-c, 2-b, 3-a, 4-d

C 1-b, 2-d, 3-c, 4-a

D 1-c, 2-a, 3-b, 4-d

💡 Short Explanation

�� Potential energy depends on orientation. �� Minimum energy corresponds to stable equilibrium. �� Maximum energy corresponds to unstable equilibrium.

✅ Correct Answer Explanation

The potential energy of a magnetic dipole in a uniform magnetic field is: U=-mBcos⁡θ For θ = 0°: U=-mB which is the minimum potential energy and represents the most stable equilibrium position. For θ = 180°: U=+mB which is the maximum potential energy and represents the most unstable equilibrium position. For θ = 90°: U=0 This corresponds to neither a maximum nor a minimum value of potential energy. For θ = 120°: U=-mBcos⁡120^∘U=-mB(, 1/2)U=mB/2 This corresponds to an arbitrary non-equilibrium state. Hence: 1 → b 2 → c 3 → d 4 → a Therefore, Option A is correct.

❓ Why Other Options Are Incorrect

�� Option B → Stable and unstable positions are interchanged.
�� Option C → U = +mB is incorrectly matched.
�� Option D → Multiple energy-state correspondences are incorrect.

🎯 Strategy

Concept Application

Application
Use U=-mBcos⁡θfor each given angle and identify the corresponding equilibrium state.
Final Logic
Minimum energy → Stable, Maximum energy → Unstable, Zero energy → Intermediate state.

🧠 Memory Trick

One Eighty Degree → Maximum

📚 Class: XII | Book: NCERT Physics Part I | Chapter: Magnetism and Matter | Topic: Potential Energy of Magnetic Dipole | Subtopic: Stability and Equilibrium

7 By utilizing the mathematical replacements from electrostatics (E → B, p → m, 1/ε₀ → μ₀), the analogous equation for the electrostatic torque p × E translates perfectly to:

A B × m

B m × B

C m · B

D μ₀(m × B)

💡 Short Explanation

�� Electric and magnetic dipoles have analogous torque equations. �� Torque is represented by a cross product. �� Direct substitution gives the magnetic form.

✅ Correct Answer Explanation

The torque acting on an electric dipole in an external electric field is: τ=p×E NCERT discusses the close analogy between electric dipoles and magnetic dipoles. Using the standard replacements: p→mE→B the corresponding magnetic torque expression becomes: τ=m×B This equation gives both the magnitude and direction of the torque experienced by a magnetic dipole in a uniform magnetic field. The magnitude is: τ=mBsin⁡θ and the direction is determined using the right-hand rule. Therefore, the correct magnetic analogue of p × E is m × B.

❓ Why Other Options Are Incorrect

�� Option A → Reversing the order changes the direction of the vector.
�� Option C → Dot product represents energy, not torque.
�� Option D → μ₀ is not part of the torque expression.

🎯 Strategy

NCERT Recall

Application
Recall the standard electrostatic-to-magnetic substitutions.
Final Logic
Replace p by m and E by B directly.

🧠 Memory Trick

Cross Means Torque

📚 Class: XII | Book: NCERT Physics Part I | Chapter: Magnetism and Matter | Topic: Dipole Analogy | Subtopic: Torque Analogy

8 Identify the correct statements regarding the conversion of constants between electrostatic and magnetic dipole analogies.
Statements:
1. The free space permittivity term 1/ε₀ is completely replaced by μ₀.
2. The 4π factor found in the denominator of electrostatic field equations remains in the denominator for magnetic field equations.
3. The relative magnetic permeability replaces the dielectric constant perfectly.
4. These replacements are strictly valid only for extremely short dipoles at very large distances (r >> l).

A 1, 3 and 4 are correct

B 1, 2 and 3 are correct

C 2, 3 and 4 are correct

D 1, 2, 3 and 4 are correct

💡 Short Explanation

�� Electric and magnetic dipole equations have similar forms. �� Constants transform systematically. �� The analogy is based on short-dipole approximations.

✅ Correct Answer Explanation

NCERT develops a mathematical analogy between electric dipoles and magnetic dipoles for points located far from the dipole. The substitutions are: E↔Bp↔m1/ε_0↔μ_0 and 1/4πε_0↔μ_0/4π Notice that the factor 4π remains unchanged in the denominator. Similarly, dielectric behavior in electrostatics corresponds conceptually to magnetic permeability in magnetism. The analogy is valid for short dipoles observed at distances much larger than the dipole length (r≫l), where dipole approximations are applicable. Therefore, all four statements are correct.

❓ Why Other Options Are Incorrect

�� Option A → Statement 2 is also correct.
�� Option B → Statement 4 is also correct.
�� Option C → Statement 1 is correct.

🎯 Strategy

NCERT Recall

Application
Recall the complete correspondence table used in dipole analogies.
Final Logic
All listed replacements follow directly from NCERT dipole analogies.

🧠 Memory Trick

Epsilon → Mu

📚 Class: XII | Book: NCERT Physics Part I | Chapter: Magnetism and Matter | Topic: Dipole Analogy | Subtopic: Mathematical Replacements

9 The dependence on distance (r) for the far axial field of a short magnetic dipole and the electric field of a short electric dipole are respectively:

A 1/r² and 1/r³

B 1/r³ and 1/r³

C 1/r² and 1/r²

D 1/r³ and 1/r²

💡 Short Explanation

�� Both are dipole fields. �� Both decrease rapidly with distance. �� Both follow inverse-cube dependence.

✅ Correct Answer Explanation

For a short magnetic dipole, the far axial magnetic field is: B_A=μ_0/4π2m/r^3 Similarly, the far axial electric field of a short electric dipole is: E_A=1/4πε_02p/r^3 In both cases, the field strength decreases as the inverse cube of the distance from the dipole. This inverse-cube dependence is a characteristic feature of dipole fields and distinguishes them from the inverse-square dependence observed for isolated charges and monopole-like sources. Therefore, both fields vary as: 1/r^3

❓ Why Other Options Are Incorrect

�� Option A → Magnetic dipole fields do not vary as 1/r².
�� Option C → Neither field follows inverse-square dependence.
�� Option D → Electric dipole fields also vary as 1/r³.

🎯 Strategy

NCERT Recall

Application
Recall the axial field expressions for electric and magnetic dipoles.
Final Logic
Both dipole fields have inverse-cube dependence.

🧠 Memory Trick

Monopole Means Square

📚 Class: XII | Book: NCERT Physics Part I | Chapter: Magnetism and Matter | Topic: Dipole Analogy | Subtopic: Distance Dependence

10 Identify the correct statements regarding the vector form of the axial field equation.
Statements:
1. The vector BA is proportional to the magnetic moment vector m.
2. The direction of the axial field is exactly parallel to the dipole moment.
3. The magnitude falls off as the inverse cube of the distance r.
4. The formula assumes that the distance r is much less than the magnet's length l.

A 1, 2 and 3 are correct

B 2, 3 and 4 are correct

C 1 and 4 are correct

D 1, 2 and 4 are correct

💡 Short Explanation

�� Axial field is proportional to m. �� Direction is along the magnetic moment. �� The dipole approximation requires r >> l.

✅ Correct Answer Explanation

The axial magnetic field of a short magnetic dipole is: B_A=μ_0/4π2m/r^3 This expression shows that the field vector is directly proportional to the magnetic moment vector. Therefore, the direction of the axial field is parallel to the magnetic moment. The magnitude decreases as: 1/r^3 which is characteristic of dipole fields. The equation is derived under the short-dipole approximation: r≫l where r is the observation distance and l is the dipole length. Therefore, Statements 1, 2 and 3 are correct, while Statement 4 is incorrect.

❓ Why Other Options Are Incorrect

�� Option B → Statement 4 is incorrect.
�� Option C → Statements 2 and 3 are also correct.
�� Option D → Statement 4 is incorrect.

🎯 Strategy

NCERT Recall

Application
Recall the vector form of the axial magnetic field equation.
Final Logic
Axial field ∝ m and decreases as 1/r³ for r >> l.

🧠 Memory Trick

Cube Law for Dipoles

📚 Class: XII | Book: NCERT Physics Part I | Chapter: Magnetism and Matter | Topic: Magnetic Dipole Field | Subtopic: Vector Form of Axial Field Equation

11 A short bar magnet has an axial magnetic field magnitude of 9.6 × 10⁻⁵ T at a distance of 10 cm. If you move to a point 10 cm away on the equatorial line, the magnitude of the field BE will be:

A 9.6 × 10⁻⁵ T

B 1.92 × 10⁻⁴ T

C 2.4 × 10⁻⁵ T

D 4.8 × 10⁻⁵ T

💡 Short Explanation

�� Axial field is twice the equatorial field. �� Both measurements are taken at the same distance. �� Use the ratio BA = 2BE.

✅ Correct Answer Explanation

For a short magnetic dipole, the magnetic fields at the axial and equatorial positions are: B_A=μ_0/4π2m/r^3B_E=μ_0/4πm/r^3 Thus, B_A=2B_E Given: B_A=9.6×10^(-5) T Therefore, B_E=B_A/2B_E=9.6×10^(-5)/2B_E=4.8×10^(-5) T Hence, the magnetic field at the equatorial position is 4.8 × 10⁻⁵ T. Unit Verification The ratio is dimensionless, so the unit remains Tesla.

❓ Why Other Options Are Incorrect

�� Option A → Axial and equatorial fields are not equal.
�� Option B → Twice the axial field value.
�� Option C → Half of the correct equatorial field.

🎯 Strategy

Substitution

Application
Use the standard NCERT relation between axial and equatorial magnetic fields.
Final Logic
B_E=B_A/2

🧠 Memory Trick

Equatorial Half

📚 Class: XII | Book: NCERT Physics Part I | Chapter: Magnetism and Matter | Topic: Magnetic Dipole Field | Subtopic: Axial and Equatorial Field Relation

12 Incorrect statement regarding the directional relationship to the magnetic moment.

A The equatorial field vector BE points opposite to the magnetic moment m.

B The negative sign in the BE formula indicates the anti-parallel configuration.

C The magnetic field lines at the equatorial plane travel from the south pole back to the north pole internally.

D The axial field vector BA aligns in the same direction as the magnetic moment m.

💡 Short Explanation

�� Equatorial field opposes m. �� Axial field aligns with m. �� Statement C incorrectly describes field-line behavior.

✅ Correct Answer Explanation

The magnetic field on the equatorial line of a short magnetic dipole is: B_E=-μ_0/4πm/r^3 The negative sign indicates that the equatorial magnetic field is opposite to the magnetic moment vector. Hence Statements A and B are correct. The axial magnetic field is: B_A=μ_0/4π2m/r^3 Therefore, the axial field points in the same direction as the magnetic moment, making Statement D correct. Statement C is incorrect because magnetic field lines outside a magnet emerge from the north pole and enter the south pole. Inside the magnet, they travel from south to north. The equatorial plane itself is not described as a region where field lines "travel from south pole back to north pole internally." Hence the statement is not a correct description of the equatorial field.

❓ Why Other Options Are Incorrect

�� Option A → Correct property of the equatorial field.
�� Option B → Negative sign denotes opposite direction.
�� Option D → Axial field is parallel to m.

🎯 Strategy

NCERT Recall

Application
Recall the vector forms of axial and equatorial magnetic fields.
Final Logic
Equatorial field opposes m while axial field aligns with m.

🧠 Memory Trick

Equatorial Opposes m

📚 Class: XII | Book: NCERT Physics Part I | Chapter: Magnetism and Matter | Topic: Magnetic Dipole Field | Subtopic: Field Directions

13 According to the dipole analogy table, the formula for the external field torque:

A highlights that both dipoles seek to align perpendicularly to their respective external fields

B demonstrates that restoring torque relies on a scalar product in both regimes

C proves that cross products govern the interaction dynamics (p × E and m × B)

D signifies that electric torque is attractive while magnetic torque is repulsive

💡 Short Explanation

�� Torque is represented by a cross product. �� Electric and magnetic dipoles show mathematical analogy. �� Cross products determine rotational effects.

✅ Correct Answer Explanation

For an electric dipole in an external electric field: τ=p×E For a magnetic dipole in an external magnetic field: τ=m×B Both expressions involve vector cross products. The magnitude of torque depends on the sine of the angle between the dipole moment and the external field: τ=pEsin⁡θ or τ=mBsin⁡θ The cross product nature of these equations shows that torque is fundamentally a rotational effect. It acts to align the dipole moment with the external field and determines the direction of rotation according to the right-hand rule. Therefore, the dipole analogy clearly demonstrates that cross products govern torque interactions in both electrostatic and magnetic systems.

❓ Why Other Options Are Incorrect

�� Option A → Dipoles tend to align parallel, not perpendicular.
�� Option B → Torque depends on a cross product, not a scalar product.
�� Option D → Torque is rotational, not attractive or repulsive.

🎯 Strategy

NCERT Recall

Application
Recall the torque expressions for electric and magnetic dipoles.
Final Logic
Torque equations use vector cross products.

🧠 Memory Trick

Dot Means Energy

📚 Class: XII | Book: NCERT Physics Part I | Chapter: Magnetism and Matter | Topic: Dipole Analogy | Subtopic: External Field Torque

14 Based on the comparison of external field energy in the dipole analogy table, the energy values at 0°, 90°, and 180°:

A evaluate respectively to minimum, zero, and maximum for both electrostatic and magnetic dipoles

B evaluate respectively to zero, minimum, and maximum for both electrostatic and magnetic dipoles

C represent only unstable configurations for any angle other than 0°

D depend strictly on the mass of the respective dipole

💡 Short Explanation

�� Energy depends on cosθ. �� Parallel alignment gives minimum energy. �� Anti-parallel alignment gives maximum energy.

✅ Correct Answer Explanation

The potential energy of a dipole in an external field is: U=-pEcos⁡θ for electric dipoles and U=-mBcos⁡θ for magnetic dipoles. At: θ=0^∘U=-pEor-mB which is the minimum energy. At: θ=90^∘U=0 At: θ=180^∘U=+pEor+mB which is the maximum energy. Thus, both electric and magnetic dipoles exhibit identical energy behavior due to the mathematical analogy.

❓ Why Other Options Are Incorrect

�� Option B → The energy at 0° is minimum, not zero.
�� Option C → Intermediate angles are not necessarily unstable.
�� Option D → Energy depends on dipole moment and field, not mass.

🎯 Strategy

Concept Application

Application
Substitute the given angles into the energy equation.
Final Logic
0° → Minimum, 90° → Zero, 180° → Maximum.

🧠 Memory Trick

Anti-parallel = Maximum

📚 Class: XII | Book: NCERT Physics Part I | Chapter: Magnetism and Matter | Topic: Potential Energy of Dipoles | Subtopic: Energy and Stability

15 Match List I (Configurations of needle Q relative to dipole P) with List II (Equilibrium Status).

List I	List II
1. Q on normal bisector, mQ parallel to BP	a. Unstable, highest potential energy on axis
2. Q on normal bisector, mQ anti-parallel to BP	b. Stable, lowest potential energy on axis
3. Q on axis, mQ parallel to BP	c. Stable, lowest potential energy on bisector
4. Q on axis, mQ anti-parallel to BP	d. Unstable, highest potential energy on bisector A.1-d, 2-c, 3-a, 4-b

A (option not parsed — please edit)

B 1-b, 2-a, 3-c, 4-d

C 1-c, 2-a, 3-b, 4-d

D 1-c, 2-d, 3-b, 4-a

💡 Short Explanation

�� Stable equilibrium occurs when the dipole aligns with the local field. �� Anti-parallel alignment gives unstable equilibrium. �� Axis and bisector fields have different directions.

✅ Correct Answer Explanation

The stability of a magnetic dipole depends on its orientation relative to the local magnetic field produced by another dipole. On the axis of dipole P, the magnetic field is directed along the magnetic moment of P. Therefore, when Q is placed on the axis and its magnetic moment is parallel to the local field, the configuration has minimum potential energy and is stable. The anti-parallel orientation corresponds to maximum potential energy and unstable equilibrium. On the normal bisector, the magnetic field is opposite to the magnetic moment of P. Consequently, a dipole aligned parallel to the local field achieves minimum potential energy and stable equilibrium, while an anti-parallel orientation gives unstable equilibrium. Thus: 1 → c 2 → d 3 → b 4 → a

❓ Why Other Options Are Incorrect

�� Option B → Axis and bisector configurations are incorrectly interchanged.
�� Option C → Unstable bisector condition is mismatched.
�� Option D → Stable and unstable states are reversed.

🎯 Strategy

Concept Application

Application
Determine the local magnetic field direction first, then apply the condition for stable equilibrium.
Final Logic
Parallel to local field → Stable; Anti-parallel to local field → Unstable.

🧠 Memory Trick

Anti-parallel Local Field = Unstable

📚 Class: XII | Book: NCERT Physics Part I | Chapter: Magnetism and Matter | Topic: Dipole-Dipole Interaction | Subtopic: Stability of Configurations

16 Identify the correct statements concerning dipole interaction and determination of stable needle orientations.
Statements:
1. The system's potential energy relies on one dipole interacting with the magnetic field produced by the other dipole.
2. Equilibrium is unstable when the secondary dipole aligns anti-parallel to the local magnetic field of the primary dipole.
3. The lowest potential energy configuration among planar orientations occurs when the dipoles are collinear and parallel.
4. The magnetic field on the normal bisector acts exactly parallel to the primary dipole's magnetic moment.

A 1, 2 and 3 are correct

B 2, 3 and 4 are correct

C 1, 3 and 4 are correct

D 1, 2 and 4 are correct

💡 Short Explanation

�� Dipole interaction energy depends on the local magnetic field. �� Anti-parallel alignment gives unstable equilibrium. �� Collinear parallel dipoles correspond to minimum energy.

✅ Correct Answer Explanation

The potential energy of a dipole system arises because one magnetic dipole experiences the magnetic field produced by the other dipole. Thus, the interaction energy is determined by: U=-m⋅B Stable equilibrium occurs when the magnetic moment aligns parallel to the local magnetic field, producing minimum potential energy. If the dipole is oriented anti-parallel to the local field, the potential energy becomes maximum and the equilibrium becomes unstable. Among common planar configurations, the lowest energy state occurs when the dipoles are arranged collinearly with their magnetic moments parallel. In this arrangement, the interaction is most favorable energetically. On the normal bisector of a dipole, however, the magnetic field is directed opposite to the magnetic moment of the primary dipole. Therefore Statement 4 is incorrect.

❓ Why Other Options Are Incorrect

�� Option B → Statement 4 is incorrect.
�� Option C → Statement 4 is incorrect.
�� Option D → Statement 4 is incorrect.

🎯 Strategy

Concept Application

Application
Determine the local magnetic field direction and apply the condition for minimum potential energy.
Final Logic
Parallel to local field gives stable equilibrium; anti-parallel gives unstable equilibrium.

🧠 Memory Trick

Anti-parallel → Unstable

📚 Class: XII | Book: NCERT Physics Part I | Chapter: Magnetism and Matter | Topic: Dipole-Dipole Interaction | Subtopic: Stable Configurations

17 Identify the correct statement regarding the dynamics of a dipole in a non-uniform magnetic field.

A The net force is zero because the opposing pole forces perfectly cancel.

B A net force exists because the magnetic field differs in magnitude at the two poles.

C The induced south pole of an iron nail is repelled by the magnet's north pole.

D Torque is entirely absent if the field is non-uniform.

💡 Short Explanation

�� Non-uniform fields produce unequal pole forces. �� Unequal forces create a net force. �� Torque may also be present.

✅ Correct Answer Explanation

In a non-uniform magnetic field, the magnetic field strength is different at different positions. Consequently, the north and south poles of a magnetic dipole experience forces of unequal magnitudes. Since the forces acting on the two poles are not equal, they do not completely cancel. As a result, the dipole experiences a net force directed toward the region of stronger magnetic field. Additionally, if the dipole is not aligned with the magnetic field, a torque may also act on it. Therefore, a dipole placed in a non-uniform magnetic field can simultaneously experience both force and torque. This behavior differs from that in a uniform magnetic field, where equal and opposite pole forces cancel, leaving only torque.

❓ Why Other Options Are Incorrect

�� Option A → This is true only for a perfectly uniform magnetic field.
�� Option C → Unlike poles attract each other.
�� Option D → Non-uniform fields can produce torque as well as force.

🎯 Strategy

NCERT Recall

Application
Compare the behavior of a dipole in uniform and non-uniform magnetic fields.
Final Logic
Unequal magnetic field strengths at the poles produce a net force.

🧠 Memory Trick

Non-uniform → Force + Torque

📚 Class: XII | Book: NCERT Physics Part I | Chapter: Magnetism and Matter | Topic: Magnetic Dipole in Magnetic Field | Subtopic: Non-Uniform Fields

18 Why does an iron nail near a bar magnet experience an attractive net force?

A Because it acts purely as a diamagnetic material perfectly repelling the field.

B Because isolated magnetic monopoles in the iron are drawn to the magnet.

C Because the torque completely transforms into a linear attractive force via the scalar product.

D Because the non-uniform field induces a magnetic moment, and the induced unlike pole is closer to the magnet.

💡 Short Explanation

�� Iron becomes magnetized by induction. �� Opposite poles are induced near the magnet. �� The closer attractive force dominates.

✅ Correct Answer Explanation

When an iron nail is brought near a bar magnet, the magnetic field of the magnet induces magnetization in the nail. The end of the nail nearest the magnet develops a magnetic pole opposite to the nearby pole of the magnet. Since the magnetic field around the magnet is non-uniform, the attractive force on the nearer induced pole is stronger than any force acting on the farther end of the nail. As magnetic force decreases rapidly with distance, the attraction at the near end dominates. Consequently, the nail experiences a net attractive force toward the magnet. This effect explains why iron objects are drawn toward permanent magnets even though they may initially be unmagnetized.

❓ Why Other Options Are Incorrect

�� Option A → Iron is not behaving as a perfect diamagnetic material.
�� Option B → Magnetic monopoles have not been observed.
�� Option C → Torque and force arise from different physical effects.

🎯 Strategy

Concept Application

Application
Analyze induced magnetization and the effect of distance-dependent magnetic forces.
Final Logic
The closer induced opposite pole experiences the stronger attraction.

🧠 Memory Trick

Induced Pole Nearer → Stronger Attraction

📚 Class: XII | Book: NCERT Physics Part I | Chapter: Magnetism and Matter | Topic: Induced Magnetism | Subtopic: Attraction of Iron Objects

19 The alignment of a small compass needle is used to visualize the magnetic field. The alignment and the net field direction are:

A Identical and Identical

B Opposite and Identical

C Orthogonal and Orthogonal

D Identical and Opposite

💡 Short Explanation

�� A compass aligns along the magnetic field. �� The needle indicates local field direction. �� Field-line mapping uses this principle.

✅ Correct Answer Explanation

A magnetic compass consists of a small magnetic dipole free to rotate. When placed in a magnetic field, it experiences a torque that aligns its magnetic moment along the local magnetic field direction. Therefore, the direction of the compass needle becomes identical to the direction of the magnetic field at that point. By placing the compass at various positions, one can determine the direction of the magnetic field throughout the surrounding space. This method forms the basis for constructing magnetic field-line diagrams around magnets, current-carrying conductors and solenoids. Hence, both the alignment of the compass needle and the net magnetic field direction are identical.

❓ Why Other Options Are Incorrect

�� Option B → The needle does not align opposite to the field.
�� Option C → The needle is not perpendicular to the field.
�� Option D → Alignment follows the field direction.

🎯 Strategy

NCERT Recall

Application
Recall how magnetic field lines are experimentally mapped.
Final Logic
Compass direction equals local magnetic field direction.

🧠 Memory Trick

Compass Shows Field

📚 Class: XII | Book: NCERT Physics Part I | Chapter: Magnetism and Matter | Topic: Magnetic Field Lines | Subtopic: Compass Method

20 Regarding self-torque and internal forces in a current-carrying wire:

A Present and Present

B Absent and Present

C Present and Absent

D Absent and Absent

💡 Short Explanation

�� A current element does not act on itself. �� Self-torque is absent. �� Different elements of the wire can interact.

✅ Correct Answer Explanation

A current element cannot exert a magnetic force or torque on itself. Therefore, self-force and self-torque are absent for an individual element of a current-carrying conductor. However, different elements of the same conductor can exert magnetic forces on one another. These internal magnetic interactions are real and contribute to the mechanical behavior of current-carrying conductors. Thus, while self-torque is absent, internal forces between different parts of the wire are present. This distinction is important in understanding the magnetic forces acting within loops, coils and other current-carrying structures. Therefore, the correct combination is: • Self-torque → Absent • Internal forces → Present

❓ Why Other Options Are Incorrect

�� Option A → Self-torque is absent.
�� Option C → Internal forces do exist.
�� Option D → Internal magnetic forces are present.

🎯 Strategy

NCERT Recall

Application
Distinguish between self-action and interaction between different current elements.
Final Logic
An element cannot act on itself, but different wire elements can interact magnetically.

🧠 Memory Trick

Internal Yes

📚 Class: XII | Book: NCERT Physics Part I | Chapter: Moving Charges and Magnetism | Topic: Magnetic Forces on Current Elements | Subtopic: Self-Torque and Internal Forces

CUET UG Physics Booster Test 3-Dipole Dynamics and Electrostatic Analogs

Test Complete!

Answer Review