CUET UG Physics Booster Test 3-Fundamentals of Electromagnetic Induction
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QUESTION 1 OF 20
Incorrect statement regarding the historical development of electromagnetism
QUESTION 2 OF 20
Correct statements about Faraday's Experiment 6.3 (Stationary coils):
1. It showed relative motion is not an absolute requirement for induction.
2. A momentary deflection occurs only when the key is pressed or released.
3. An iron rod inserted into the coils decreases the deflection dramatically.
QUESTION 3 OF 20
Regarding the core concept of induction:
1. It relies strictly on the conservation of charge.
2. An emf is induced whenever magnetic flux through a circuit changes.
3. Induced emf is produced even if the circuit is open.
Choose correct:
QUESTION 4 OF 20
Match List I (Experiment Setup) with List II (Current Behavior)
| List I (Experiment Setup) | List II (Current Behavior) |
|---|---|
| (1) Coil C₁ fixed, C₂ (with steady current) moves towards C₁ | (a) Current is induced in C₁ |
| (2) Tapping key K connecting stationary C₂ to battery is held pressed | (b) Current in C₁ drops to zero |
| (3) Key K is just pressed in stationary C₂ circuit | (c) Momentary current is induced in C₁ |
| (4) Key K is released from stationary C₂ circuit | (d) Momentary current is induced in opposite direction in C₁ |
QUESTION 5 OF 20
Definition of Flux statements:
1. It is defined similarly to electric flux.
2. It measures the magnetic field mathematically across a given area.
3. It is maximized when the area vector is perpendicular to the magnetic field.
QUESTION 6 OF 20
Which mathematical operation correctly proves that magnetic flux is a scalar nature?
QUESTION 7 OF 20
A circular coil of radius 10 cm, 500 turns, and resistance 2 Ω is placed with its plane perpendicular to the horizontal component of the earth's magnetic field (3.0 × 10⁻⁵ T). If rotated by 180° in 0.25 s, what is the magnitude of the estimated induced current? (π ≈ 3.14)
QUESTION 8 OF 20
SI Unit Weber is equivalent to which combination of SI units for Magnetic field and Area respectively?
QUESTION 9 OF 20
When calculating flux through a complex surface, assigning an area vector dAᵢ to each element ensures that
QUESTION 10 OF 20
Incorrect statement regarding the angle theta in the flux equation
QUESTION 11 OF 20
Match List I (Parameter Changed) with List II (Effect on Induced EMF in a Constant B-Field)
| List I (Parameter Changed) | List II (Effect on Induced EMF) |
|---|---|
| (1) Shrinking the coil | (a) Non-zero emf induced |
| (2) Holding the coil stationary | (b) Zero emf induced |
| (3) Rotating the coil in the magnetic field | (c) Non-zero emf induced |
| (4) Increasing the area of the coil | (d) Non-zero emf induced |
QUESTION 12 OF 20
Correct statements for a plane surface flux:
1. A constant steady field through a stationary plane loop does not induce an emf.
2. If the loop's area changes, the flux changes.
3. Flux is calculated by BA cos θ.
QUESTION 13 OF 20
Regarding integration over an area for flux calculation:
1 It is mathematically represented as a summation of elements over a complex surface.
2 It is only required when the field is uniform.
3 It handles variations in both the magnitude and direction of the magnetic field.
Choose correct:
QUESTION 14 OF 20
If the magnetic field Bᵢ over a surface area element dAᵢ = 2.0 cm² changes from 2.0 T to 4.0 T in a direction parallel to the area vector, what is the change in flux through this specific element?
QUESTION 15 OF 20
When evaluating magnetic flux through a curved surface, the surface must be conceptually broken down because
QUESTION 16 OF 20
If a surface comprises N discrete flat area elements dAᵢ, and the field Bᵢ is constant over each element, the integral for flux simplifies to
QUESTION 17 OF 20
Role of varying fields in induction:
1. A changing magnetic field can exert a force on a stationary charge.
2. A time-varying magnetic field generates an electric field.
3. Moving charges in a static field and static charges in a time-varying field both relate to Faraday's law.
QUESTION 18 OF 20
In Faraday's law, ε = -N (dΦ_B / dt), the variables N and dt represent respectively:
QUESTION 19 OF 20
Correct statements about relative motion principles:
1. Moving coil towards magnet induces current.
2. Moving magnet towards coil induces current.
3. Moving a current-carrying coil towards another coil induces current.
QUESTION 20 OF 20
Incorrect statement regarding coil and magnet interactions in Faraday's experiments
Test Complete!
Answer Review
1 Incorrect statement regarding the historical development of electromagnetism
�� Oersted discovered magnetic effect of current. �� Faraday and Henry discovered electromagnetic induction. �� Oersted did not prove induction.
- Oersted demonstrated that electric current produces a magnetic effect. → Ampere further developed the relationship between electricity and magnetism. → The converse phenomenon, namely production of current by changing magnetic fields, was discovered independently by Michael Faraday and Joseph Henry. → Therefore statement B is historically incorrect.
- �� Option A → Correct historical contribution of Oersted and Ampere.
- �� Option C → Correct; both independently discovered induction.
- �� Option D → Correct; electricity and magnetism were once viewed separately.
Used
- �� Elimination
Application:
- �� Identify which scientist actually discovered electromagnetic induction.
Final Logic:
- �� Faraday and Henry, not Oersted, discovered induction.
- Oersted: Current → Magnet; Faraday: Magnet → Current
2 Correct statements about Faraday's Experiment 6.3 (Stationary coils):
1. It showed relative motion is not an absolute requirement for induction.
2. A momentary deflection occurs only when the key is pressed or released.
3. An iron rod inserted into the coils decreases the deflection dramatically.
�� Flux change is essential. �� Pressing or releasing key changes current. �� Iron core increases induction.
- In Faraday's stationary-coil experiment, induction occurred without mechanical motion. → The induced current appeared only when the current in the neighboring coil changed. → Deflection occurred momentarily during pressing or releasing of the key. → An iron rod enhances magnetic flux linkage and increases, not decreases, deflection.
- �� Option B → Statement 3 is false.
- �� Option C → Statement 3 is false.
- �� Option D → Includes incorrect statement 3.
Used
- �� Elimination
Application:
- �� Check the effect of an iron core on magnetic flux.
Final Logic:
- �� Iron core strengthens induction; therefore statement 3 is wrong.
- Iron Core = More Flux
3 Regarding the core concept of induction:
1. It relies strictly on the conservation of charge.
2. An emf is induced whenever magnetic flux through a circuit changes.
3. Induced emf is produced even if the circuit is open.
Choose correct:
�� Flux change induces emf. �� Closed circuit is required for current, not emf. �� Conservation of charge is not the primary basis.
- Faraday's law states that a changing magnetic flux induces emf. → Induced emf exists whether the circuit is open or closed. → In an open circuit, emf is produced but current cannot flow. → Statement 1 is incorrect because induction is governed by changing magnetic flux, not solely conservation of charge.
- �� Option A → Includes incorrect statement 1.
- �� Option C → Statement 1 is false.
- �� Option D → Statement 1 remains incorrect.
Used
- �� Elimination
Application:
- �� Distinguish between induced emf and induced current.
Final Logic:
- �� Flux change creates emf even without a closed conducting path.
- EMF First, Current Later
4 Match List I (Experiment Setup) with List II (Current Behavior)
| List I (Experiment Setup) | List II (Current Behavior) |
|---|---|
| (1) Coil C₁ fixed, C₂ (with steady current) moves towards C₁ | (a) Current is induced in C₁ |
| (2) Tapping key K connecting stationary C₂ to battery is held pressed | (b) Current in C₁ drops to zero |
| (3) Key K is just pressed in stationary C₂ circuit | (c) Momentary current is induced in C₁ |
| (4) Key K is released from stationary C₂ circuit | (d) Momentary current is induced in opposite direction in C₁ |
Electromagnetic induction occurs only when magnetic flux changes. Relative motion between coils changes flux and induces current. A steady current produces constant flux and no sustained induction. Making or breaking the circuit produces momentary induction.
- When C₂ moves towards C₁, the magnetic flux linked with C₁ changes continuously. → Therefore, a current is induced in C₁. → When the key K remains pressed, current in C₂ becomes steady after a short time. → The magnetic flux then becomes constant, so the induced current in C₁ drops to zero. → When the key is just pressed, current in C₂ rises from zero to a finite value. → This changing current produces a changing magnetic flux, causing a momentary induced current in C₁. → When the key is released, current in C₂ falls to zero. → The magnetic flux decreases, producing a momentary induced current in the opposite direction. Therefore: 1 → a 2 → b 3 → c 4 → d Hence, Option A is correct.
- Option B: Reverses the observations for moving coil and steady-current cases.
- Option C: Incorrectly assigns induction to the steady-current condition.
- Option D: Incorrectly matches the directions and nature of induced currents.
Used
- Matching / Flux-Change Analysis
Application:
- Determine whether the magnetic flux linked with C₁ is changing or constant.
Final Logic:
- Changing flux → Induced current.
- Constant flux → No induced current.
- Increasing and decreasing flux produce opposite current directions.
"Make → Induce, Break → Reverse"
5 Definition of Flux statements:
1. It is defined similarly to electric flux.
2. It measures the magnetic field mathematically across a given area.
3. It is maximized when the area vector is perpendicular to the magnetic field.
�� Flux is analogous to electric flux. �� Measures magnetic field through a surface. �� Maximum flux occurs when area vector is parallel to field.
- Magnetic flux is defined as Φ = B·A. → It measures magnetic field passing through a surface. → Maximum flux occurs when θ = 0° between B and area vector. → Therefore statement 3 is incorrect.
- �� Option B → Includes false statement 3.
- �� Option C → Includes false statement 3.
- �� Option D → Includes false statement 3.
Used
- �� Elimination
Application:
- �� Recall condition for maximum value of cos θ.
Final Logic:
- �� Maximum flux occurs when B and A are parallel.
- Max Flux → B ∥ A
6 Which mathematical operation correctly proves that magnetic flux is a scalar nature?
�� Flux = B·A. �� Dot product gives scalar quantity. �� Therefore flux is scalar.
- Magnetic flux is defined as: Φ = B·A → Since dot product always produces a scalar quantity, magnetic flux is scalar. → This directly establishes the scalar nature of flux.
- �� Option A → Cross product gives vector.
- �� Option C → Vector addition does not define flux.
- �� Option D → Not used in flux definition.
Used
- �� Conceptual Recall
Application:
- �� Recall mathematical definition of magnetic flux.
Final Logic:
- �� Dot product yields scalar flux.
- Dot ⇒ Scalar
7 A circular coil of radius 10 cm, 500 turns, and resistance 2 Ω is placed with its plane perpendicular to the horizontal component of the earth's magnetic field (3.0 × 10⁻⁵ T). If rotated by 180° in 0.25 s, what is the magnitude of the estimated induced current? (π ≈ 3.14)
�� ΔΦ = 2BA per turn. �� Use Faraday's law. �� I = ε/R.
- Area = π(0.1)² = 0.01π m² → Change in flux per turn: ΔΦ = 2BA = 2 × (3×10⁻⁵) × (0.01π) ≈ 1.884 ×10⁻⁶ Wb → Total induced emf: ε = NΔΦ/Δt = 500×1.884×10⁻⁶ /0.25 ≈ 3.77×10⁻³ V → Current: I = ε/R ≈ (3.77×10⁻³)/2 ≈ 1.89×10⁻³ A
- �� Option B → Equals emf value, not current.
- �� Option C → Ten times larger.
- �� Option D → Twenty times larger.
Used
- �� Substitution
Application:
- �� Apply Faraday's law and Ohm's law sequentially.
Final Logic:
- �� Numerical calculation gives 1.9 × 10⁻³ A.
- Flux Change → EMF → Current
8 SI Unit Weber is equivalent to which combination of SI units for Magnetic field and Area respectively?
�� Φ = BA. �� Unit of B = Tesla. �� Unit of A = m².
- Magnetic flux: Φ = BA → SI unit: Wb = T × m² → Hence Weber corresponds to Tesla multiplied by square meter.
- �� Option B → Gauss is CGS unit.
- �� Option C → Area requires m².
- �� Option D → Dimensionally incorrect.
Used
- �� Dimensional/Unit Analysis
Application:
- �� Derive units directly from flux formula.
Final Logic:
- �� Wb = Tm².
- Weber = Tesla × Area
9 When calculating flux through a complex surface, assigning an area vector dAᵢ to each element ensures that
�� Curved surfaces have varying normals. �� Each element gets its own area vector. �� Accurate flux calculation becomes possible.
- Different portions of a complex or curved surface possess different orientations. → Assigning dAᵢ to each element accounts for the local normal direction. → This allows correct evaluation of B·dA over the surface.
- �� Option B → Flux remains scalar.
- �� Option C → Surface does not alter field lines.
- �� Option D → No such cancellation occurs.
Used
- �� Conceptual Recall
Application:
- �� Recall meaning of elemental area vectors.
Final Logic:
- �� Local normals are required for accurate integration.
- dA Tracks Direction
10 Incorrect statement regarding the angle theta in the flux equation
�� Flux = BA cosθ. �� cos90° = 0. �� Maximum flux occurs at θ = 0°.
- Magnetic flux is: Φ = BA cosθ → At θ = 90°: Φ = 0 → Maximum flux occurs when θ = 0°. → Therefore statement B is incorrect.
- �� Option A → Correct consequence of rotation.
- �� Option C → Correct definition of θ.
- �� Option D → Changing θ changes flux and can induce emf.
Used
- �� Substitution
Application:
- �� Compare flux values at θ = 0° and 90°.
Final Logic:
- �� cos0° > cos90°, so maximum flux occurs at 0°.
- 90° = Zero Flux
11 Match List I (Parameter Changed) with List II (Effect on Induced EMF in a Constant B-Field)
| List I (Parameter Changed) | List II (Effect on Induced EMF) |
|---|---|
| (1) Shrinking the coil | (a) Non-zero emf induced |
| (2) Holding the coil stationary | (b) Zero emf induced |
| (3) Rotating the coil in the magnetic field | (c) Non-zero emf induced |
| (4) Increasing the area of the coil | (d) Non-zero emf induced |
Induced emf is produced when magnetic flux changes. Changing the area or orientation of a coil changes magnetic flux. A stationary coil with fixed area and orientation has constant flux. Constant flux means no induced emf.
- Magnetic flux through a coil is given by: Φ = BA cosθ where (B) is the magnetic field, (A) is the area of the coil, and (\theta) is the angle between the magnetic field and the area vector. → Shrinking the coil decreases the area (A), causing the magnetic flux to change with time. → Therefore, a non-zero emf is induced. → Holding the coil stationary with unchanged area and orientation in a constant magnetic field keeps the magnetic flux constant. → Hence, zero emf is induced. → Rotating the coil changes the angle (\theta), thereby changing the magnetic flux. → Therefore, a non-zero emf is induced. → Increasing the area of the coil also changes the magnetic flux. → Hence, a non-zero emf is induced. Therefore: 1 → a 2 → b 3 → c 4 → d Hence, Option A is correct.
- Option B: Incorrectly assigns zero emf to a shrinking coil and non-zero emf to a stationary coil.
- Option C: Incorrectly assigns zero emf to a rotating coil.
- Option D: Does not correctly match the effects produced by changes in area and orientation.
Used
- Matching / Flux Analysis
Application:
- Use the relation (\Phi = BA\cos\theta).
- Check whether (A) or (\theta) changes with time.
Final Logic:
- Change in area or orientation → Change in flux → Induced emf.
- No change in flux → No induced emf.
"Constant Flux = Zero EMF"
12 Correct statements for a plane surface flux:
1. A constant steady field through a stationary plane loop does not induce an emf.
2. If the loop's area changes, the flux changes.
3. Flux is calculated by BA cos θ.
�� Constant flux produces no emf. �� Area affects flux. �� Flux formula is BA cosθ.
- Statement 1 is correct because induction requires changing flux. → Statement 2 is correct since flux depends on area. → Statement 3 is the standard flux relation for a uniform magnetic field. → Therefore all three statements are correct.
- �� Option A → Omits statement 3.
- �� Option B → Omits statement 2.
- �� Option C → Omits statement 1.
Used
- �� Elimination
Application:
- �� Verify each statement using the flux equation and Faraday's law.
Final Logic:
- �� All three statements agree with NCERT definitions.
- Flux Depends on B, A and θ
13 Regarding integration over an area for flux calculation:
1 It is mathematically represented as a summation of elements over a complex surface.
2 It is only required when the field is uniform.
3 It handles variations in both the magnitude and direction of the magnetic field.
Choose correct:
�� Integration sums elemental contributions. �� Needed for non-uniform fields and complex surfaces. �� Handles varying magnitude and direction.
- Flux through a complex surface is evaluated by dividing it into infinitesimal elements. → Integration is the limiting form of summing elemental flux contributions. → It accommodates variations in magnetic field strength and direction. → Statement 2 is incorrect because integration is especially useful when the field is non-uniform.
- �� Option A → Statement 2 is false.
- �� Option C → Statement 2 is false.
- �� Option D → Statement 1 is also correct.
Used
- �� Elimination
Application:
- �� Identify the purpose of surface integration.
Final Logic:
- �� Integration handles complex surfaces and varying fields.
- Complex Surface → Integrate
14 If the magnetic field Bᵢ over a surface area element dAᵢ = 2.0 cm² changes from 2.0 T to 4.0 T in a direction parallel to the area vector, what is the change in flux through this specific element?
�� ΔΦ = ΔB × A �� Area vector parallel to B. �� θ = 0°.
- Area: A = 2.0 cm² = 2 × 10⁻⁴ m² → Change in field: ΔB = 4 − 2 = 2 T → Since B is parallel to area vector: ΔΦ = ΔB × A = 2 × 2 × 10⁻⁴ = 4 × 10⁻⁴ Wb
- �� Option B → Uses only one factor incorrectly.
- �� Option C → Double the correct value.
- �� Option D → Incorrect unit magnitude.
Used
- �� Substitution
Application:
- �� Apply ΔΦ = AΔB cosθ.
Final Logic:
- �� θ = 0° gives ΔΦ = 4 × 10⁻⁴ Wb.
- Parallel ⇒ cos0° = 1
15 When evaluating magnetic flux through a curved surface, the surface must be conceptually broken down because
�� Different points have different normals. �� One area vector is insufficient. �� Infinitesimal vectors are used.
- A curved surface does not possess one unique normal direction. → Different regions have different orientations. → Therefore the surface is divided into infinitesimal elements, each with its own area vector. → Flux is then calculated by integration.
- �� Option B → No such property exists.
- �� Option C → Field lines are not forced to follow surface geometry.
- �� Option D → Curved surfaces can have non-zero flux.
Used
- �� Conceptual Recall
Application:
- �� Recall the definition of area vector on curved surfaces.
Final Logic:
- �� Curved surfaces require many local area vectors.
- Curved Surface = Many Normals
16 If a surface comprises N discrete flat area elements dAᵢ, and the field Bᵢ is constant over each element, the integral for flux simplifies to
�� Flux is sum of elemental contributions. �� Each element contributes Bᵢ·dAᵢ. �� Integral becomes summation.
- The flux through an infinitesimal element is: dΦ = Bᵢ·dAᵢ → Total flux equals the sum over all elements. → For discrete elements: Φ = Σ Bᵢ·dAᵢ → Therefore option B is correct.
- �� Option A → Ignores vector orientation.
- �� Option C → Valid only under special uniform conditions.
- �� Option D → Not a flux expression.
Used
- �� Conceptual Recall
Application:
- �� Recall discrete form of surface integration.
Final Logic:
- �� Flux equals sum of elemental dot products.
- Total Flux = Sum of Tiny Fluxes
17 Role of varying fields in induction:
1. A changing magnetic field can exert a force on a stationary charge.
2. A time-varying magnetic field generates an electric field.
3. Moving charges in a static field and static charges in a time-varying field both relate to Faraday's law.
A changing magnetic field produces an induced electric field. The induced electric field can exert a force on stationary charges. Both motional emf and induced emf due to changing magnetic fields are explained by Faraday's law.
- According to Faraday's law, a time-varying magnetic field generates an electric field. → The induced electric field can act on charges even when they are initially stationary, causing them to move. → Thus, a changing magnetic field can effectively produce a force on stationary charges through the induced electric field. → Moving charges in a static magnetic field produce motional emf, while stationary charges in a time-varying magnetic field experience transformer emf. → Both situations are manifestations of electromagnetic induction described by Faraday's law. → Therefore, statements 1, 2, and 3 are correct.
- Option A: Excludes statement 3, which is correct.
- Option B: Excludes statement 1, which is correct in the context of the induced electric field produced by a changing magnetic field.
- Option C: Excludes statement 2, which is a direct consequence of Faraday's law.
Used
- Conceptual Analysis
Application:
- Apply Faraday's law to understand the consequences of a time-varying magnetic field.
- Relate induced electric fields to the motion of charges and electromagnetic induction.
Final Logic:
- Changing magnetic field → Induced electric field.
- Induced electric field → Force on charges.
- Both motional and transformer emf arise from Faraday's law.
"Faraday Links Motion and Variation"
18 In Faraday's law, ε = -N (dΦ_B / dt), the variables N and dt represent respectively:
�� N = turns in coil. �� dt = infinitesimal time interval. �� Appears in rate of flux change.
- N represents the total number of turns linked with magnetic flux. → dt represents a very small time interval over which flux changes. → The expression gives induced emf proportional to the rate of flux change.
- �� Option A → N does not represent poles.
- �� Option C → N is not Newton.
- �� Option D → N is not flux.
Used
- �� Conceptual Recall
Application:
- �� Recall standard form of Faraday's law.
Final Logic:
- �� N counts turns and dt measures time interval.
- N = Number of Turns
19 Correct statements about relative motion principles:
1. Moving coil towards magnet induces current.
2. Moving magnet towards coil induces current.
3. Moving a current-carrying coil towards another coil induces current.
�� Relative motion changes flux. �� Coil or magnet may move. �� Mutual induction also occurs.
- Moving a coil toward a magnet changes magnetic flux. → Moving a magnet toward a coil also changes flux. → Bringing a current-carrying coil near another coil changes linked magnetic flux and induces current. → Therefore all three statements are correct.
- �� Option A → Omits statement 3.
- �� Option B → Omits statement 1.
- �� Option C → Omits statement 2.
Used
- �� Elimination
Application:
- �� Check whether flux changes in each case.
Final Logic:
- �� Every situation involves changing flux linkage.
- Relative Motion = Induction
20 Incorrect statement regarding coil and magnet interactions in Faraday's experiments
�� Pole reversal reverses current direction. �� Faster motion increases emf. �� Opposite motions produce opposite deflections.
- The direction of induced current depends on the direction of flux change. → Bringing a North pole and bringing a South pole toward the coil produce opposite flux changes. → Therefore galvanometer deflections occur in opposite directions. → Hence statement B is incorrect.
- �� Option A → Correct; current exists while flux changes.
- �� Option C → Faster motion increases rate of flux change.
- �� Option D → Opposite motions produce opposite current directions.
Used
- �� Contextual/Tonal Matching
Application:
- �� Analyze direction of magnetic flux change.
Final Logic:
- �� Opposite poles produce opposite induced current directions.
- Reverse Pole → Reverse Deflection
