CUET UG Physics Booster Test 2-Electromagnetic Wave Theory
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QUESTION 1 OF 20
Consider the charge radiation statements. Choose the correct statements.
1. A proton moving at a constant velocity of 2 × 10⁵ m/s produces EM waves.
2. An electron oscillating harmonically at 1 MHz produces EM waves of 1 MHz.
3. A stationary charge produces a time-varying magnetic field.
4. The energy of the propagating wave comes at the expense of the source's energy.
QUESTION 2 OF 20
An electric dipole forms a basic source of EM waves only when its charges are in ______ motion; the resulting radiation wavelength is typically correlated with the ______ of the radiating system.
QUESTION 3 OF 20
In the mechanism of wave propagation, the regenerating electric and magnetic fields
QUESTION 4 OF 20
Identify the incorrect statement about self-sustaining oscillations
QUESTION 5 OF 20
If an electron in a linear antenna oscillates completely 500,000 times per second, the resulting radio wave's angular frequency ω in rad/s will be
QUESTION 6 OF 20
Impracticality of generating visible light using a standard AC electronic circuit
1. Visible light has a frequency around 6 × 10¹⁴ Hz.
2. Modern electronic circuits cap out around 10¹¹ Hz.
3. Circuits can only generate magnetic waves, not electric waves.
4. Wavelength of yellow light is too large for an antenna.
QUESTION 7 OF 20
Choose the correct statements about the speed of light in vacuum
1. It varies based on whether the wave is an X-ray or visible light.
2. It is used to define the standard of length because of its measured constancy.
3. It is independent of the wavelength of the electromagnetic wave.
4. Its value is exactly 1 / √(μ₀ε₀).
QUESTION 8 OF 20
Match List I with List II
| List I | List II |
|---|---|
| 1. Speed of light in vacuum (c) | a. √(με/μ₀ε₀) |
| 2. Speed of EM wave in a medium (v) | b. 1/√(μ₀ε₀) |
| 3. Refractive index (c/v) | c. c |
| 4. Ratio of amplitudes (E₀/B₀) | d. 1/√(με) |
QUESTION 9 OF 20
If a plane electromagnetic wave of frequency 30 MHz is traveling in a vacuum, what will be the magnitude of the wave vector k?
(c = 3 × 10⁸ m/s)
QUESTION 10 OF 20
If the magnetic field of a wave is given by B = B₀ sin(kx + ωt) ĵ, the wave propagates in the direction of
QUESTION 11 OF 20
Identify the incorrect statement about the electric-magnetic ratio when E₀ = 60 V/m
QUESTION 12 OF 20
Consider the sinusoidal wave function statements. Choose the correct statements:
Ex = E₀ sin(kz − ωt)
1. The magnetic field must oscillate in the y-z plane.
2. The magnetic field is given by By = B₀ sin(kz − ωt).
3. The phase difference between the oscillating E and B fields is π.
4. The wave propagates along the +z direction.
QUESTION 13 OF 20
The fundamental property that electric and magnetic fields in an EM wave are perpendicular to each other and to the direction of propagation proves that
QUESTION 14 OF 20
If B is along the +x-axis and the wave propagates along the +y-axis, E must be along the ______ axis, because E × B yields ______.
QUESTION 15 OF 20
If a medium has a magnetic permeability μ = μ₀ and an electric permittivity ε = 4ε₀, what will be the velocity of EM waves in this medium?
(c = 3 × 10⁸ m/s)
QUESTION 16 OF 20
When an EM wave passes from vacuum into a material medium with refractive index n = 1.5
1. Its velocity decreases to 2 × 10⁸ m/s.
2. Its frequency remains unchanged.
3. Its velocity increases to 4.5 × 10⁸ m/s.
4. Its wavelength in the medium is greater than in a vacuum.
QUESTION 17 OF 20
Match List I with List II
| List I | List II |
|---|---|
| 1. Microwave oven | a. Raises temperature of molecules/substances |
| 2. Infrared therapy lamps | b. Transfers energy to earth making life possible |
| 3. X-ray machines | c. Matches resonant frequency of water molecules to transfer kinetic energy |
| 4. Photosynthesis (Visible light) | d. Damages or destroys living tissues at high energy |
QUESTION 18 OF 20
Choose the correct statements about solar EM wave impact
1. The earth absorbs incoming visible light and re-radiates it as longer wavelength infrared radiation.
2. Greenhouse gases directly trap incoming visible radiation before it reaches the surface.
3. This absorption process plays an important role in maintaining the earth's average temperature.
4. Infrared radiation from the sun is entirely blocked by the ozone layer.
QUESTION 19 OF 20
Hertz's successful 1887 experiment was pivotal because it transferred theoretical physics into reality by verifying that
QUESTION 20 OF 20
Consider the Radio wave production statements. Choose the correct statements:
1. They are produced by accelerated motion of charges in conducting wires.
2. The FM radio band operates at higher frequencies than the AM band.
3. They are utilized by cellular phones in the UHF band.
4. They typically originate directly from atomic nuclei.
Test Complete!
Answer Review
1 Consider the charge radiation statements. Choose the correct statements.
1. A proton moving at a constant velocity of 2 × 10⁵ m/s produces EM waves.
2. An electron oscillating harmonically at 1 MHz produces EM waves of 1 MHz.
3. A stationary charge produces a time-varying magnetic field.
4. The energy of the propagating wave comes at the expense of the source's energy.
�� Accelerated charges radiate. �� Radiation frequency equals source frequency. �� Energy carried by waves comes from the source.
Statement 2 is correct because an oscillating electron emits electromagnetic waves having the same frequency as its oscillation. Statement 4 is correct because electromagnetic waves transport energy away from the source, reducing the source's energy. Statement 1 is incorrect because a charge moving with constant velocity does not radiate. Statement 3 is incorrect because a stationary charge produces only a static electric field and no magnetic field.
- �� Option A → Includes Statements 1 and 3.
- �� Option C → Includes Statement 1.
- �� Option D → Includes Statement 3.
Used
- Elimination
Application:
- Remove statements involving non-accelerating charges.
Final Logic:
- Only Statements 2 and 4 are correct.
Acceleration → Radiation
2 An electric dipole forms a basic source of EM waves only when its charges are in ______ motion; the resulting radiation wavelength is typically correlated with the ______ of the radiating system.
�� Radiation requires acceleration. �� Oscillating dipoles are EM wave sources. �� Antenna size is linked to wavelength.
An oscillating dipole contains accelerating charges, which generate electromagnetic radiation. The wavelength of emitted radiation is commonly related to the characteristic dimensions of the radiating system, such as antenna length. Therefore Option B is correct.
- �� Option A → Uniform motion does not radiate.
- �� Option C → Stationary charges do not radiate.
- �� Option D → Temperature is not the relevant parameter here.
Used
- Contextual/Tonal Matching
Application:
- Apply the physical requirements for radiation.
Final Logic:
- Accelerated charges and system size determine radiation characteristics.
Dipole + Acceleration = EM Waves
3 In the mechanism of wave propagation, the regenerating electric and magnetic fields
�� Changing E produces B. �� Changing B produces E. �� No medium is required.
According to Maxwell's theory, a time-varying electric field generates a magnetic field, and a time-varying magnetic field generates an electric field. This mutual regeneration enables electromagnetic waves to propagate through vacuum without any material medium. Therefore Option D is correct.
- �� Option A → No mechanical force is needed.
- �� Option B → Free-space propagation requires no conduction current.
- �� Option C → The fields continuously influence one another.
Used
- Contextual/Tonal Matching
Application:
- Apply Maxwell's field regeneration principle.
Final Logic:
- Mutual induction sustains propagation.
E → B → E → B
4 Identify the incorrect statement about self-sustaining oscillations
�� EM waves are self-sustaining. �� No conduction current is needed in vacuum. �� Maxwell's equations explain propagation.
Electromagnetic waves propagate in free space because changing electric and magnetic fields continuously regenerate each other. No conduction current exists in vacuum, and none is required for propagation. Therefore Option D is incorrect.
- �� Option A → Correct statement.
- �� Option B → Correct role of displacement current.
- �� Option C → Correct statement of Faraday's law.
Used
- Odd One Out
Application:
- Identify the statement contradicting free-space propagation.
Final Logic:
- Conduction current is unnecessary in vacuum.
Vacuum Needs No Current
5 If an electron in a linear antenna oscillates completely 500,000 times per second, the resulting radio wave's angular frequency ω in rad/s will be
�� Frequency = 5 × 10⁵ Hz. �� ω = 2πν. �� Substitute directly.
Given: ν = 500,000 Hz = 5 × 10⁵ Hz Angular frequency: ω = 2πν = 2π × 5 × 10⁵ = 10⁶π rad/s Hence Option B is correct.
- �� Option A → Missing factor of 2.
- �� Option C → Half the correct value.
- �� Option D → π omitted.
Used
- Substitution
Application:
- Use ω = 2πν.
Final Logic:
- ω = 10⁶π rad/s.
ω = 2πν
6 Impracticality of generating visible light using a standard AC electronic circuit
1. Visible light has a frequency around 6 × 10¹⁴ Hz.
2. Modern electronic circuits cap out around 10¹¹ Hz.
3. Circuits can only generate magnetic waves, not electric waves.
4. Wavelength of yellow light is too large for an antenna.
�� Visible light frequency is extremely high. �� Electronic circuits cannot reach optical frequencies. �� Statements 3 and 4 are incorrect.
Statement 1 is correct because visible light frequencies are approximately 10¹⁴–10¹⁵ Hz. Statement 2 is correct because ordinary electronic circuits generally operate up to about 10¹¹ Hz. Statement 3 is incorrect because electromagnetic waves contain both electric and magnetic fields. Statement 4 is incorrect because visible-light wavelengths are very small, not large.
- �� Option A → Includes Statement 4.
- �� Option B → Includes Statement 3.
- �� Option D → Both statements are incorrect.
Used
- Elimination
Application:
- Select only physically correct reasons.
Final Logic:
- Frequency limitation is the real reason.
10¹¹ vs 10¹⁴
7 Choose the correct statements about the speed of light in vacuum
1. It varies based on whether the wave is an X-ray or visible light.
2. It is used to define the standard of length because of its measured constancy.
3. It is independent of the wavelength of the electromagnetic wave.
4. Its value is exactly 1 / √(μ₀ε₀).
�� Speed in vacuum is constant. �� Independent of wavelength. �� Given by Maxwell's relation.
Statements 2, 3 and 4 are correct. The speed of light is constant in vacuum and equals: c = 1/√(μ₀ε₀) This value is used in defining the metre. Statement 1 is incorrect because all electromagnetic waves travel at the same speed in vacuum.
- �� Option A → Includes Statement 1.
- �� Option C → Includes Statement 1.
- �� Option D → Statement 1 is false.
Used
- Elimination
Application:
- Reject options containing Statement 1.
Final Logic:
- Vacuum speed is independent of wavelength.
All EM Waves → Same c
8 Match List I with List II
| List I | List II |
|---|---|
| 1. Speed of light in vacuum (c) | a. √(με/μ₀ε₀) |
| 2. Speed of EM wave in a medium (v) | b. 1/√(μ₀ε₀) |
| 3. Refractive index (c/v) | c. c |
| 4. Ratio of amplitudes (E₀/B₀) | d. 1/√(με) |
�� c = 1/√(μ₀ε₀) �� v = 1/√(με) �� E₀/B₀ = c
1 → b 2 → d 3 → a 4 → c Therefore: P-b, Q-d, R-a, S-c Hence Option A is correct.
- �� Option B → Incorrect c and v matches.
- �� Option C → Incorrect refractive-index match.
- �� Option D → Multiple mismatches.
Used
- Option Grouping
Application:
- Match standard electromagnetic-wave formulas.
Final Logic:
- Only Option A satisfies all relations.
c, v, n, E/B
9 If a plane electromagnetic wave of frequency 30 MHz is traveling in a vacuum, what will be the magnitude of the wave vector k?
(c = 3 × 10⁸ m/s)
�� λ = c/ν �� k = 2π/λ �� Use vacuum speed.
Given: ν = 30 MHz = 3 × 10⁷ Hz λ = c/ν = (3 × 10⁸)/(3 × 10⁷) = 10 m Therefore, k = 2π/λ = 2π/10 = 0.2π rad/m Hence Option A is correct.
- �� Option B → Three times larger than actual value.
- �� Option C → Incorrect wavelength calculation.
- �� Option D → Fifteen times larger than actual value.
Used
- Substitution
Application:
- Compute λ first, then k.
Final Logic:
- k = 0.2π rad/m.
k = 2π/λ
10 If the magnetic field of a wave is given by B = B₀ sin(kx + ωt) ĵ, the wave propagates in the direction of
�� Wave form determines direction. �� kx − ωt → +x direction. �� kx + ωt → −x direction.
A wave traveling in the negative x-direction is represented by sin(kx + ωt) whereas sin(kx − ωt) represents propagation in the positive x-direction. Hence Option B is correct.
- �� Option A → Corresponds to kx − ωt.
- �� Option C → Wave propagates along x, not y.
- �� Option D → Not along y-axis.
Used
- Formula Recall
Application:
- Recall the standard traveling-wave forms.
Final Logic:
- Plus sign with ωt implies motion along −x.
(kx + ωt) → Backward
11 Identify the incorrect statement about the electric-magnetic ratio when E₀ = 60 V/m
�� E₀ = cB₀. �� E₀/B₀ = c. �� B₀/E₀ = 1/c.
For an electromagnetic wave: E₀ = cB₀ Therefore, B₀ = E₀/c = 60/(3 × 10⁸) = 2 × 10⁻⁷ T Hence Statement A is correct. Also, E₀/B₀ = c = 3 × 10⁸ m/s Therefore Statements B and D are correct. However, B₀/E₀ = 1/c = 3.33 × 10⁻⁹ s/m and not 3 × 10⁸ m/s. Hence Statement C is incorrect.
- �� Option A → Correctly calculates B₀.
- �� Option B → Correct relation.
- �� Option D → Standard EM wave relation.
Used
- Substitution
Application:
- Apply E₀ = cB₀ and evaluate each statement.
Final Logic:
- Only Statement C reverses the ratio incorrectly.
E/B = c
12 Consider the sinusoidal wave function statements. Choose the correct statements:
Ex = E₀ sin(kz − ωt)
1. The magnetic field must oscillate in the y-z plane.
2. The magnetic field is given by By = B₀ sin(kz − ωt).
3. The phase difference between the oscillating E and B fields is π.
4. The wave propagates along the +z direction.
�� E and B oscillate in phase. �� Wave travels along +z. �� B is along y-direction.
For Ex = E₀ sin(kz − ωt) the wave propagates in the +z direction. The magnetic field is perpendicular to both E and the propagation direction, so: By = B₀ sin(kz − ωt) Thus Statements 2 and 4 are correct. Statement 1 is incorrect because B oscillates along the y-axis, not in the y-z plane. Statement 3 is incorrect because E and B are in phase (phase difference = 0).
- �� Option B → Includes Statements 1 and 3.
- �� Option C → Includes Statement 3.
- �� Option D → Includes Statement 1.
Used
- Elimination
Application:
- Remove options containing Statements 1 or 3.
Final Logic:
- Only Statements 2 and 4 are correct.
E and B: Same Phase
13 The fundamental property that electric and magnetic fields in an EM wave are perpendicular to each other and to the direction of propagation proves that
�� E ⊥ B. �� E and B ⊥ propagation direction. �� This is the defining feature of transverse waves.
In electromagnetic waves: E ⊥ B E ⊥ propagation direction B ⊥ propagation direction Since oscillations occur perpendicular to the direction of propagation, EM waves are transverse waves. Therefore Option C is correct.
- �� Option A → Describes longitudinal waves.
- �� Option B → Not implied by field geometry.
- �� Option D → EM waves need no material medium.
Used
- Contextual/Tonal Matching
Application:
- Identify the wave type from field orientation.
Final Logic:
- Perpendicular oscillations imply transverse waves.
Perpendicular = Transverse
14 If B is along the +x-axis and the wave propagates along the +y-axis, E must be along the ______ axis, because E × B yields ______.
�� Propagation direction = E × B. �� Use right-hand rule. �� E × B must point along +y.
Given: B → +x Propagation → +y We require: E × (+x) = +y Using vector products: (-z) × (+x) = +y Therefore E must be along the -z direction. Hence the correct option is: B. -z, +y
- �� Option A → (+z) × (+x) = -y.
- �� Option C → Gives wrong propagation direction.
- �� Option D → Gives -y direction.
Used
- Vector Analysis
Application:
- Apply right-hand-rule cross product.
Final Logic:
- (-z) × (+x) = +y.
E × B = Direction
15 If a medium has a magnetic permeability μ = μ₀ and an electric permittivity ε = 4ε₀, what will be the velocity of EM waves in this medium?
(c = 3 × 10⁸ m/s)
�� v = 1/√(με) �� Compare with vacuum speed. �� ε becomes four times larger.
v = 1/√(με) = 1/√(μ₀ × 4ε₀) = 1/(2√(μ₀ε₀)) = c/2 = (3 × 10⁸)/2 = 1.5 × 10⁸ m/s Hence Option B is correct.
- �� Option A → Vacuum speed.
- �� Option C → Exceeds vacuum speed.
- �� Option D → Extra factor of 2 error.
Used
- Substitution
Application:
- Substitute μ and ε into the velocity formula.
Final Logic:
- v = c/2.
ε ×4 ⇒ v ÷2
16 When an EM wave passes from vacuum into a material medium with refractive index n = 1.5
1. Its velocity decreases to 2 × 10⁸ m/s.
2. Its frequency remains unchanged.
3. Its velocity increases to 4.5 × 10⁸ m/s.
4. Its wavelength in the medium is greater than in a vacuum.
�� v = c/n. �� Frequency remains constant. �� Wavelength decreases.
Given: n = 1.5 v = c/n = (3 × 10⁸)/1.5 = 2 × 10⁸ m/s Thus Statement 1 is correct. Frequency remains unchanged at a boundary, so Statement 2 is correct. Statement 3 is incorrect because velocity decreases. Statement 4 is incorrect because wavelength decreases in the medium.
- �� Option A → Includes Statement 4.
- �� Option B → Includes Statement 3.
- �� Option D → Statements 3 and 4 are both incorrect.
Used
- Substitution
Application:
- Use n = c/v and wave-boundary principles.
Final Logic:
- Velocity decreases, frequency remains constant.
Medium: v↓, λ↓, f Same
17 Match List I with List II
| List I | List II |
|---|---|
| 1. Microwave oven | a. Raises temperature of molecules/substances |
| 2. Infrared therapy lamps | b. Transfers energy to earth making life possible |
| 3. X-ray machines | c. Matches resonant frequency of water molecules to transfer kinetic energy |
| 4. Photosynthesis (Visible light) | d. Damages or destroys living tissues at high energy |
�� Microwaves heat water. �� Infrared provides thermal effects. �� X-rays can damage tissue. �� Photosynthesis supports life.
1 → c : Microwave oven 2 → a : Infrared therapy lamps 3 → d : X-ray machines 4 → b : Photosynthesis Thus: 1-c, 2-a, 3-d, 4-b Hence Option A is correct.
- �� Option B → Multiple mismatches.
- �� Option C → Incorrect therapy and photosynthesis pairing.
- �� Option D → Incorrect microwave and X-ray pairing.
Used
- Option Grouping
Application:
- Match each EM wave application with its effect.
Final Logic:
- Only Option A correctly matches all pairs.
Micro-Water, IR-Heat, X-Ray-Damage, Light-Life
18 Choose the correct statements about solar EM wave impact
1. The earth absorbs incoming visible light and re-radiates it as longer wavelength infrared radiation.
2. Greenhouse gases directly trap incoming visible radiation before it reaches the surface.
3. This absorption process plays an important role in maintaining the earth's average temperature.
4. Infrared radiation from the sun is entirely blocked by the ozone layer.
�� Earth reradiates absorbed energy as IR. �� Greenhouse effect regulates temperature. �� Statements 2 and 4 are incorrect.
Statement 1 is correct because Earth absorbs solar radiation and reradiates energy mainly in the infrared region. Statement 3 is correct because greenhouse warming helps maintain Earth's average temperature. Statement 2 is incorrect because greenhouse gases mainly absorb outgoing infrared radiation rather than incoming visible light. Statement 4 is incorrect because ozone primarily absorbs ultraviolet radiation.
- �� Option A → Includes Statement 2.
- �� Option B → Both statements are incorrect.
- �� Option D → Includes incorrect statements.
Used
- Elimination
Application:
- Reject scientifically incorrect atmospheric interactions.
Final Logic:
- Only Statements 1 and 3 are correct.
Sunlight In, IR Out
19 Hertz's successful 1887 experiment was pivotal because it transferred theoretical physics into reality by verifying that
�� Hertz verified Maxwell's prediction. �� Electromagnetic waves exist. �� Waves propagate independently through space.
Hertz experimentally generated and detected electromagnetic waves, confirming Maxwell's prediction that oscillating electric and magnetic fields can travel through space as self-propagating waves. Therefore Option B is correct.
- �� Option A → Uniform motion does not produce radiation.
- �� Option C → Free space supports all EM frequencies.
- �� Option D → Not the objective of Hertz's experiment.
Used
- Contextual/Tonal Matching
Application:
- Identify the key outcome of Hertz's experiment.
Final Logic:
- Hertz experimentally confirmed electromagnetic waves.
Hertz = Proof of Maxwell
20 Consider the Radio wave production statements. Choose the correct statements:
1. They are produced by accelerated motion of charges in conducting wires.
2. The FM radio band operates at higher frequencies than the AM band.
3. They are utilized by cellular phones in the UHF band.
4. They typically originate directly from atomic nuclei.
�� Radio waves come from accelerating charges. �� FM frequencies exceed AM frequencies. �� Cellular communication uses radio frequencies.
Statement 1 is correct because radio waves are generated by accelerating charges in antennas. Statement 2 is correct because FM broadcasting operates at frequencies much higher than AM broadcasting. Statement 3 is correct because cellular communication commonly uses frequencies within the UHF region. Statement 4 is incorrect because radio waves used in communication are not normally produced by atomic nuclei.
- �� Option B → Includes Statement 4.
- �� Option C → Includes Statement 4.
- �� Option D → Includes Statement 4.
Used
- Elimination
Application:
- Remove all options containing Statement 4.
Final Logic:
- Communication radio waves originate from accelerated charges, not nuclei.
Antenna → Radio Waves
