CUET UG Physics Booster Test 2-Fundamentals of Electromagnetic Induction
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QUESTION 1 OF 20
Regarding the historical discoveries of Oersted and Ampere:
1 They established that electricity and magnetism are inter-related.
2 They found that moving electric charges produce magnetic fields.
3 They demonstrated that changing magnetic fields produce electric currents.
QUESTION 2 OF 20
Match List I (Scientist) with List II (Region of Work in 1830s)
| List I (Scientist) | List II (Country) |
|---|---|
| (1) Michael Faraday | (a) England |
| (2) Joseph Henry | (b) USA |
| (3) Hans Christian Oersted | (c) Denmark |
| (4) André-Marie Ampère | (d) France |
QUESTION 3 OF 20
Incorrect statement about electromagnetic induction
QUESTION 4 OF 20
Induced electric currents in a coil:
1 Deflection is larger when the magnet is pushed faster.
2 Reversing the magnet's poles reverses the deflection direction.
3 Current lasts permanently even after the magnet stops.
QUESTION 5 OF 20
If a square loop of side 10 cm is placed vertically in the east-west plane, and a uniform magnetic field of 0.10 T is set up across the plane in the north-east direction, what is the initial magnetic flux? (cos 45° ≈ 0.707)
QUESTION 6 OF 20
Nature of magnetic flux and magnetic field respectively:
QUESTION 7 OF 20
In the flux equation Φ_B = B · A, if the plane of the coil is parallel to the magnetic field, the flux through the coil is
QUESTION 8 OF 20
The SI unit weber (Wb) can also be dimensionally equivalent to
QUESTION 9 OF 20
Correct statements about the area vector:
(1) It has a magnitude equal to the surface area.
(2) Its direction is parallel to the surface.
(3) Its direction is conceptually managed as a vector to define orientation.
QUESTION 10 OF 20
A circular coil of radius 10 cm is placed with its plane perpendicular to a magnetic field of 3.0 × 10⁻⁵ T. It is rotated by 180°. The change in magnitude of angle theta alters the flux. What is the initial flux? (π ≈ 3.14)
QUESTION 11 OF 20
Incorrect statement about a constant magnetic field through a plane:
QUESTION 12 OF 20
For a plane surface of area A placed in a uniform magnetic field B, the maximum flux occurs when the angle θ between B and A is
QUESTION 13 OF 20
When evaluating flux over a non-uniform field, the total surface is divided into small area elements dAᵢ so that
QUESTION 14 OF 20
When the magnetic field magnitude is variable over a surface:
(1) Equation ΦB = BA cos θ can be directly applied without integration.
(2) The magnetic field Bᵢ must be defined at each i-th area element.
(3) The total flux is the scalar sum of fluxes through all area elements.
Choose correct:
QUESTION 15 OF 20
Flux through curved surfaces:
(1) Requires extending the basic plane surface equation.
(2) Requires treating the surface as a collection of infinitesimal area vectors.
(3) Results in a vector quantity overall.
QUESTION 16 OF 20
In the equation ΦB = Σ Bᵢ · dAᵢ, the dot product ensures that
QUESTION 17 OF 20
In Faraday's experiments, what happens to current when the key in a neighboring coil is held pressed continuously, and when it is released, respectively?
QUESTION 18 OF 20
Correct statements regarding the time rate of change of flux:
1 It induces an emf in the circuit.
2 The magnitude of induced emf is equal to it.
3 A higher rate of change yields a smaller emf.
QUESTION 19 OF 20
Incorrect statement regarding relative motion in induction:
QUESTION 20 OF 20
Match List I (Action) with List II (Observation in Galvanometer)
| List I (Action) | List II (Observation in Galvanometer) |
|---|---|
| (1) Magnet pushed towards coil | (a) Momentary deflection |
| (2) Magnet held stationary inside coil | (b) Zero deflection |
| (3) Magnet pulled away from coil | (c) Momentary deflection in opposite direction |
| (4) Coil moved towards stationary magnet | (d) Momentary deflection |
Test Complete!
Answer Review
1 Regarding the historical discoveries of Oersted and Ampere:
1 They established that electricity and magnetism are inter-related.
2 They found that moving electric charges produce magnetic fields.
3 They demonstrated that changing magnetic fields produce electric currents.
�� Oersted discovered magnetic effect of current. �� Ampere explained interaction between currents and magnetic fields. �� Changing magnetic field producing current was shown later by Faraday and Henry.
- Oersted observed that a current-carrying conductor deflects a magnetic needle, proving a relationship between electricity and magnetism. → Ampere established that electric currents produce magnetic fields and interact magnetically. → Statement 3 is incorrect because electromagnetic induction was discovered later by Faraday and Henry, not by Oersted and Ampere. → Therefore, statements 1 and 2 are correct while 3 is not.
- �� Option A → Ignores statement 2, which is also correct.
- �� Option C → Includes statement 3, which was not demonstrated by Oersted and Ampere.
- �� Option D → Incorrect because statement 3 belongs to Faraday's work.
Used
- �� Elimination
Application:
- �� Identify which scientist discovered electromagnetic induction and eliminate options containing statement 3.
Final Logic:
- �� Oersted and Ampere established the link between electricity and magnetism, but electromagnetic induction was discovered later.
- Oersted–Ampere = Current → Magnet
2 Match List I (Scientist) with List II (Region of Work in 1830s)
| List I (Scientist) | List II (Country) |
|---|---|
| (1) Michael Faraday | (a) England |
| (2) Joseph Henry | (b) USA |
| (3) Hans Christian Oersted | (c) Denmark |
| (4) André-Marie Ampère | (d) France |
Faraday was an English scientist. Henry was an American scientist. Oersted was a Danish physicist. Ampère was a French physicist and mathematician.
- Michael Faraday carried out his electromagnetic induction experiments in England. → Joseph Henry independently discovered electromagnetic induction in the USA. → Hans Christian Oersted discovered the magnetic effect of electric current in Denmark. → André-Marie Ampère developed the mathematical theory of electromagnetism in France. Therefore: 1 → a 2 → b 3 → c 4 → d Hence, Option B is correct.
- Option A: Interchanges the countries of Faraday and Henry.
- Option C: Interchanges the countries of Oersted and Ampère.
- Option D: Contains both of the above mismatches.
Used
- Historical Matching / Direct Recall
Application:
- Recall the nationality of each scientist associated with the development of electromagnetism.
Final Logic:
- Faraday → England
- Henry → USA
- Oersted → Denmark
- Ampère → France
"F-H-O-A → England-USA-Denmark-France"
3 Incorrect statement about electromagnetic induction
�� Electromagnetic induction has vast practical applications. �� Generators operate on this principle. �� Faraday and Henry demonstrated the phenomenon.
- Electromagnetic induction is one of the most useful discoveries in physics. → Electric generators, transformers and power production systems are based on it. → Statements A, C and D are correct. → Statement B is incorrect because electromagnetic induction is fundamental to modern electrical technology.
- �� Option A → Correct definition of electromagnetic induction.
- �� Option C → Modern generators are based on electromagnetic induction.
- �� Option D → Historically correct.
Used
- �� Elimination
Application:
- �� Identify the statement that contradicts known applications of induction.
Final Logic:
- �� A phenomenon powering generators cannot be merely academic.
- Induction = Generator Principle
4 Induced electric currents in a coil:
1 Deflection is larger when the magnet is pushed faster.
2 Reversing the magnet's poles reverses the deflection direction.
3 Current lasts permanently even after the magnet stops.
�� Faster motion causes larger flux change. �� Pole reversal changes current direction. �� Current exists only during flux change.
- Induced current depends on the rate of change of magnetic flux. → Faster movement increases flux change rate and therefore increases galvanometer deflection. → Reversing magnet poles reverses flux change direction and induced current direction. → When the magnet stops, flux becomes constant and current ceases.
- �� Option B → Includes incorrect statement 3.
- �� Option C → Includes incorrect statement 3.
- �� Option D → Statement 3 is false.
Used
- �� Elimination
Application:
- �� Check whether flux continues changing after motion stops.
Final Logic:
- �� No flux change means no induced current.
- Change Flux → Current Flows
5 If a square loop of side 10 cm is placed vertically in the east-west plane, and a uniform magnetic field of 0.10 T is set up across the plane in the north-east direction, what is the initial magnetic flux? (cos 45° ≈ 0.707)
�� Area = (0.1)² = 0.01 m² �� Flux = BA cosθ �� θ = 45°
- Area of square loop: A = (0.1)² = 0.01 m² → Magnetic flux: Φ = BA cos45° = 0.10 × 0.01 × 0.707 = 0.707 × 10⁻³ Wb → Hence option B is correct.
- �� Option A → Assumes cosθ = 1.
- �� Option C → Ten times larger than actual value.
- �� Option D → Ignores area and angular dependence.
Used
- �� Substitution
Application:
- �� Directly substitute numerical values into Φ = BA cosθ.
Final Logic:
- �� Numerical evaluation gives 0.707 × 10⁻³ Wb.
- Flux = BACos
6 Nature of magnetic flux and magnetic field respectively:
�� Flux is a scalar quantity. �� Magnetic field has magnitude and direction. �� Flux arises from a dot product.
- Magnetic flux is defined as Φ = B·A. → Dot product produces a scalar quantity. → Magnetic field B possesses both magnitude and direction, making it a vector. → Therefore flux is scalar while magnetic field is vector.
- �� Option B → Magnetic field is not scalar.
- �� Option C → Flux is not vector.
- �� Option D → Flux remains scalar.
Used
- �� Conceptual Recall
Application:
- �� Recall properties of dot product.
Final Logic:
- �� Dot product ⇒ scalar flux.
- Dot Product = Scalar Output
7 In the flux equation Φ_B = B · A, if the plane of the coil is parallel to the magnetic field, the flux through the coil is
�� Area vector is perpendicular to plane. �� B becomes perpendicular to area vector. �� cos90° = 0.
- Magnetic flux is Φ = BA cosθ, where θ is the angle between B and area vector. → If the plane is parallel to B, then the area vector is perpendicular to B. → Therefore θ = 90°. → Φ = BA cos90° = 0.
- �� Option A → Applies when θ = 0°.
- �� Option C → No basis in flux formula.
- �� Option D → Flux cannot become infinite.
Used
- �� Contextual/Tonal Matching
Application:
- �� Relate plane orientation to area vector orientation.
Final Logic:
- �� Plane parallel to field ⇒ area vector perpendicular ⇒ zero flux.
- Parallel Plane = Zero Flux
8 The SI unit weber (Wb) can also be dimensionally equivalent to
�� Φ = BA �� Unit of B = tesla. �� Unit of area = m².
- Magnetic flux: Φ = BA → Unit: Wb = T × m² → Therefore one weber is dimensionally equivalent to tesla meter squared.
- �� Option A → Missing one meter factor.
- �� Option C → Incorrect dimensions.
- �� Option D → Incorrect dimensions.
Used
- �� Dimensional/Unit Analysis
Application:
- �� Derive unit directly from flux formula.
Final Logic:
- �� Wb = Tm².
- Weber = Tesla × Area
9 Correct statements about the area vector:
(1) It has a magnitude equal to the surface area.
(2) Its direction is parallel to the surface.
(3) Its direction is conceptually managed as a vector to define orientation.
�� Magnitude equals area. �� Direction is normal to surface. �� Used to define orientation.
- Area vector magnitude equals the area of the surface. → Its direction is perpendicular (normal) to the surface, not parallel. → The vector representation helps define orientation of the surface in space. → Thus statements (1) and (3) are correct.
- �� Option A → Statement (2) is incorrect.
- �� Option C → Statement (2) is incorrect.
- �� Option D → Includes false statement (2).
Used
- �� Elimination
Application:
- �� Recall standard definition of area vector.
Final Logic:
- �� Area vector is normal to the surface.
- Area Vector = Area Normal
10 A circular coil of radius 10 cm is placed with its plane perpendicular to a magnetic field of 3.0 × 10⁻⁵ T. It is rotated by 180°. The change in magnitude of angle theta alters the flux. What is the initial flux? (π ≈ 3.14)
�� Area = πr² �� r = 0.1 m �� Plane ⟂ field ⇒ maximum flux
- Area of coil: A = π(0.1)² = 0.01π m² → Since plane is perpendicular to magnetic field, area vector is parallel to B. → θ = 0° → Φ = BA = (3 × 10⁻⁵)(0.01π) = 3π × 10⁻⁷ Wb → Therefore option A is correct.
- �� Option B → Double the correct value.
- �� Option C → Half the correct value.
- �� Option D → Flux is maximum, not zero.
Used
- �� Substitution
Application:
- �� Compute area and substitute into Φ = BA cosθ.
Final Logic:
- �� θ = 0° gives maximum flux = 3π × 10⁻⁷ Wb.
- Plane ⟂ B ⇒ Maximum Flux
11 Incorrect statement about a constant magnetic field through a plane:
�� Induced emf requires changing magnetic flux. �� A constant magnetic field gives constant flux in a stationary loop. �� Constant flux produces no emf.
- According to Faraday's law, induced emf exists only when magnetic flux changes with time. → A stationary loop in Earth's steady magnetic field experiences constant flux. → Since dΦ/dt = 0, induced emf is zero. → Statements A, C and D correctly describe magnetic flux and induction. → Therefore statement B is incorrect.
- �� Option A → Correct; unchanged flux means no induction.
- �� Option C → Standard magnetic flux formula.
- �� Option D → Flux must change through motion, rotation, deformation, or field variation.
Used
- �� Elimination
Application:
- �� Check which statement violates Faraday's law.
Final Logic:
- �� Constant magnetic field + stationary loop ⇒ no flux change ⇒ no emf.
- No Change = No Induction
12 For a plane surface of area A placed in a uniform magnetic field B, the maximum flux occurs when the angle θ between B and A is
�� Flux = BA cos θ. �� Maximum value of cos θ is 1. �� cos 0° = 1.
- Magnetic flux through a surface is given by: Φ = BA cos θ where θ is the angle between magnetic field B and area vector A. → Maximum flux occurs when cos θ is maximum. → cos 0° = 1, which gives: Φmax = BA → Therefore θ = 0° gives maximum magnetic flux.
- �� Option A → cos 90° = 0, giving zero flux.
- �� Option B → Gives maximum negative flux, not maximum positive flux.
- �� Option D → Produces only BA/√2.
Used
- �� Substitution
Application:
- �� Compare values of cos θ for given angles.
Final Logic:
- �� Maximum flux corresponds to maximum cosine value.
- Maximum Flux ⇒ B ∥ Area Vector
13 When evaluating flux over a non-uniform field, the total surface is divided into small area elements dAᵢ so that
�� Non-uniform fields vary from point to point. �� Small elements simplify calculations. �� Integration adds contributions from all elements.
- In a non-uniform magnetic field, B changes across the surface. → The surface is divided into infinitesimal area elements dAᵢ. → Over each tiny element, the field can be treated as approximately constant. → Flux through each element is calculated and summed using integration. → Hence option A is correct.
- �� Option B → Flux remains scalar.
- �� Option C → Field need not be zero at boundaries.
- �� Option D → Area elements never overlap.
Used
- �� Conceptual Recall
Application:
- �� Recall the purpose of infinitesimal area elements in integration.
Final Logic:
- �� Small elements allow local uniformity assumptions.
- Tiny Area → Easy Integration
14 When the magnetic field magnitude is variable over a surface:
(1) Equation ΦB = BA cos θ can be directly applied without integration.
(2) The magnetic field Bᵢ must be defined at each i-th area element.
(3) The total flux is the scalar sum of fluxes through all area elements.
Choose correct:
�� Variable fields require integration. �� Each area element has its own Bᵢ. �� Flux contributions are summed.
- For a variable magnetic field, the simple formula Φ = BA cosθ is not generally applicable. → The field value must be specified for each infinitesimal area element. → Total flux is obtained by summing all elemental flux contributions. → Therefore statements (2) and (3) are correct while statement (1) is incorrect.
- �� Option A → Statement (1) is false.
- �� Option C → Statement (1) is false.
- �� Option D → Ignores statement (2), which is necessary.
Used
- �� Elimination
Application:
- �� Identify whether integration is required in a non-uniform field.
Final Logic:
- �� Variable B requires elemental treatment and summation.
- Variable B ⇒ Integrate
15 Flux through curved surfaces:
(1) Requires extending the basic plane surface equation.
(2) Requires treating the surface as a collection of infinitesimal area vectors.
(3) Results in a vector quantity overall.
�� Curved surfaces are divided into small elements. �� Each element has its own area vector. �� Flux remains scalar.
- For curved surfaces, different parts have different orientations. → The surface is divided into infinitesimal area vectors dA. → Flux is obtained by integrating B·dA over the entire surface. → Magnetic flux remains a scalar quantity. → Hence statements (1) and (2) are correct while (3) is incorrect.
- �� Option B → Includes incorrect statement 3.
- �� Option C → Includes incorrect statement 3.
- �� Option D → Flux is not a vector.
Used
- �� Elimination
Application:
- �� Recall that dot product always yields a scalar.
Final Logic:
- �� Curved surface treatment changes calculation method, not nature of flux.
- Curved Surface → Tiny Vectors
16 In the equation ΦB = Σ Bᵢ · dAᵢ, the dot product ensures that
�� Dot product selects parallel components. �� Area vector is normal to the surface. �� Normal component of B contributes.
- Flux through an area element is: dΦ = B·dA = B dA cosθ → Since dA is normal to the surface, only the component of B along dA contributes. → This is equivalent to considering the component of magnetic field perpendicular to the surface. → Hence option B is correct.
- �� Option A → Area vector itself is fixed by geometry.
- �� Option C → Dot product produces a scalar.
- �� Option D → Directional information is included through the dot product.
Used
- �� Conceptual Recall
Application:
- �� Recall physical meaning of vector dot product.
Final Logic:
- �� Only normal component of B contributes to flux.
- Flux Uses B⊥ Surface
17 In Faraday's experiments, what happens to current when the key in a neighboring coil is held pressed continuously, and when it is released, respectively?
�� Constant current produces constant flux. �� No flux change means no induced current. �� Releasing the key changes current suddenly.
- When the key is continuously pressed, current becomes steady. → Steady current creates a constant magnetic field and constant flux. → Therefore induced current disappears after the initial transient. → When the key is released, current falls abruptly, changing magnetic flux. → This produces a momentary induced current.
- �� Option B → Reverses the observations.
- �� Option C → No steady induced current exists.
- �� Option D → Release of key definitely changes flux.
Used
- �� Contextual/Tonal Matching
Application:
- �� Identify situations where magnetic flux changes.
Final Logic:
- �� Only changing current produces induction.
- Change Current → Change Flux
18 Correct statements regarding the time rate of change of flux:
1 It induces an emf in the circuit.
2 The magnitude of induced emf is equal to it.
3 A higher rate of change yields a smaller emf.
�� Faraday's law relates emf to dΦ/dt. �� Larger flux change rate gives larger emf. �� Statement 3 is false.
- Faraday's law states: |ε| = |dΦ/dt| → Therefore a changing magnetic flux induces emf. → The magnitude of induced emf equals the rate of change of flux. → Increasing the rate of flux change increases emf. → Hence statements 1 and 2 are correct.
- �� Option B → Statement 3 is incorrect.
- �� Option C → Statement 2 is correct and cannot be omitted.
- �� Option D → Includes false statement 3.
Used
- �� Elimination
Application:
- �� Use Faraday's law directly.
Final Logic:
- �� Greater dΦ/dt gives greater emf.
- Fast Flux Change = Big EMF
19 Incorrect statement regarding relative motion in induction:
�� Induction depends on relative motion. �� Equal-speed motion gives no relative motion. �� No flux change means no induction.
- Induced current arises when magnetic flux linked with a circuit changes. → If a magnet and coil move together with the same speed and direction, their relative positions remain unchanged. → Consequently, magnetic flux remains constant. → Therefore, no induced current is produced. → Hence statement C is incorrect.
- �� Option A → Relative motion changes flux.
- �� Option B → Relative motion changes flux.
- �� Option D → Changing mutual flux between coils can induce current.
Used
- �� Elimination
Application:
- �� Check whether relative motion exists.
Final Logic:
- �� No relative motion ⇒ No flux change ⇒ No induction.
- Relative Motion Matters
20 Match List I (Action) with List II (Observation in Galvanometer)
| List I (Action) | List II (Observation in Galvanometer) |
|---|---|
| (1) Magnet pushed towards coil | (a) Momentary deflection |
| (2) Magnet held stationary inside coil | (b) Zero deflection |
| (3) Magnet pulled away from coil | (c) Momentary deflection in opposite direction |
| (4) Coil moved towards stationary magnet | (d) Momentary deflection |
A changing magnetic flux induces current in the coil. Relative motion between the magnet and coil changes the magnetic flux. Constant magnetic flux produces no induced current. Hence, motion causes galvanometer deflection, while no motion causes zero deflection.
- When a magnet is pushed towards the coil, the magnetic flux linked with the coil increases. → This produces an induced current and hence a momentary deflection in the galvanometer. → When the magnet is held stationary inside the coil, the magnetic flux remains constant. → Therefore, no induced current is produced and the galvanometer shows zero deflection. → When the magnet is pulled away from the coil, the magnetic flux decreases. → This produces an induced current in the opposite direction, causing a momentary deflection in the opposite direction. → When the coil is moved towards a stationary magnet, the magnetic flux changes due to relative motion. → Hence, a momentary deflection is observed. Therefore: 1 → a 2 → b 3 → c 4 → d Hence, Option A is correct.
- Option B: Incorrectly assigns zero deflection to a moving magnet and deflection to a stationary magnet.
- Option C: Incorrectly assigns opposite-direction deflection to a stationary magnet and zero deflection to a moving magnet.
- Option D: Incorrectly matches the observations for the moving magnet and pulled-away magnet cases.
Used
- Matching / Elimination
Application:
- Check whether the magnetic flux linked with the coil changes.
- If flux changes → induced current → galvanometer deflection.
- If flux remains constant → no induced current → zero deflection.
Final Logic:
- Relative motion causes induction.
- No relative motion causes no induction.
"No Flux Change → No Current Change"
