Cuestionario: Electromagnetic Waves — 23 preguntas

1. What electromagnetic relationship did Maxwell add to complement Faraday’s law?

A. A static electric field generates a changing magnetic field

B. A time-varying magnetic field generates an electric field

C. A static magnetic field generates a changing electric field

D. A time-varying electric field generates a magnetic field

Answer: (D)

Explicación

Maxwell showed that a time-varying electric field generates a magnetic field, complementing Faraday’s result that a changing magnetic field generates an electric field.

2. What do Maxwell’s equations together with the Lorentz force formula provide?

A. A description of gravitational fields and particle trajectories

B. A formula for conduction current without describing electromagnetic fields

C. A model of light that excludes electric and magnetic fields

D. The basic laws of electromagnetism and the force on charged particles

Answer: (D)

Explicación

Maxwell’s equations describe electromagnetic fields and their sources, while the Lorentz force gives the force exerted on a charged particle. Together they express the basic laws of electromagnetism.

3. Why did Maxwell conclude that light is an electromagnetic wave?

A. Its magnetic field remained constant while its electric field varied

B. Its measured speed was much lower than the predicted wave speed

C. Its predicted speed was close to the measured speed of light

D. It could travel only through conducting materials

Answer: (C)

Explicación

Maxwell predicted electromagnetic waves traveling at nearly 3 × 10^8 m/s, matching the measured speed of light. This led him to identify light as an electromagnetic wave.

4. Which expression defines the displacement current associated with a changing electric field?

A. i_d = dε₀/(Φ_E dt)

B. i_d = Φ_E/(ε₀t)

C. i_d = ε₀Φ_E dt

D. i_d = ε₀ dΦ_E/dt

Answer: (D)

Explicación

Displacement current is defined by i_d = ε₀ dΦ_E/dt, so it arises from a time-varying electric flux rather than from charges flowing through a conductor.

5. During capacitor charging, how does the displacement current between the plates compare with the conduction current in the connecting wire?

A. It equals the conduction current in the connecting wire

B. It exists only after the conduction current has stopped

C. It is always twice the conduction current in the wire

D. It is zero while the conduction current increases

Answer: (A)

Explicación

As the capacitor charges, the changing plate charge changes the electric flux between the plates. The resulting displacement current equals the conduction current in the connecting wire.

6. In a charging-capacitor circuit, what are the currents between the plates?

A. i_c = i and i_d = 0

B. i_c = 0 and i_d = 0

C. i_c = 0 and i_d = i

D. i_c = i and i_d = i

Answer: (C)

Explicación

Between the capacitor plates there is no charge flow, so i_c = 0, but the changing electric field produces displacement current equal to the circuit current, so i_d = i.

7. How is total current related to conduction current and displacement current?

A. i = i_c/i_d

B. i = ε₀ dΦ_E/dt − i_c

C. i = i_c − i_d

D. i = i_c + i_d = i_c + ε₀ dΦ_E/dt

Answer: (D)

Explicación

The total current is the sum of conduction and displacement currents: i = i_c + i_d = i_c + ε₀ dΦ_E/dt.

8. Which equation expresses the Ampere–Maxwell law?

A. ∮ B · dl = ε₀(i_c + μ₀ dΦ_E/dt)

B. ∮ B · dl = μ₀i_c

C. ∮ E · dl = μ₀(i_c + ε₀ dΦ_E/dt)

D. ∮ B · dl = μ₀(i_c + ε₀ dΦ_E/dt)

Answer: (D)

Explicación

The Ampere–Maxwell law states that the circulation of the magnetic field equals μ₀ times the sum of conduction and displacement currents.

9. Which type of charge motion produces electromagnetic radiation?

A. A charge moving uniformly

B. A charge with constant position

C. An accelerated charge

D. A stationary charge

Answer: (C)

Explicación

Accelerated charges produce time-varying electric and magnetic fields that radiate electromagnetic waves. Stationary or uniformly moving charges produce fields that do not vary with time in the required way.

10. How does an oscillating charge generate an electromagnetic wave?

A. Its electric field produces a magnetic field, and the two fields regenerate each other

B. Its electric field becomes a gravitational field that travels outward

C. Its charge is converted directly into a material wave

D. Its magnetic field remains constant while its electric field disappears

Answer: (A)

Explicación

An oscillating charge produces an oscillating electric field, which produces an oscillating magnetic field; these fields continually regenerate each other as the wave propagates.

11. What determines the frequency of an electromagnetic wave emitted by an oscillating charge?

A. The distance from the charge to the observer

B. The oscillation frequency of the charge

C. The strength of Earth's magnetic field

D. The amplitude of the charge's oscillation

Answer: (B)

Explicación

The emitted electromagnetic wave has the same frequency as the oscillating charge that produces it.

12. In a plane electromagnetic wave, how are the electric field, magnetic field, and propagation direction oriented?

A. The electric field is parallel to propagation, while the magnetic field is perpendicular

B. They are mutually perpendicular

C. The electric and magnetic fields are parallel, while propagation is perpendicular to both

D. They are all parallel to one another

Answer: (B)

Explicación

The electric field, magnetic field, and direction of propagation are mutually perpendicular in a plane electromagnetic wave.

13. For a wave propagating in the z-direction described by the standard field representation, which field directions are correct?

A. The electric field is along x and the magnetic field is along z

B. The electric field is along y and the magnetic field is along z

C. The electric field is along z and the magnetic field is along x

D. The electric field is along x and the magnetic field is along y

Answer: (D)

Explicación

For propagation in the z-direction, the representation uses an electric field component along x and a magnetic field component along y.

14. If the electric-field amplitude of an electromagnetic wave is E₀, what is its magnetic-field amplitude in vacuum?

A. B₀=E₀/c

B. B₀=cE₀

C. B₀=E₀+c

D. B₀=E₀c²

Answer: (A)

Explicación

The amplitudes satisfy B₀=E₀/c, so the magnetic-field amplitude is the electric-field amplitude divided by the speed of light.

15. What determines the speed of an electromagnetic wave in vacuum?

A. The wave's amplitude and frequency

B. The vacuum permittivity and permeability

C. The material density of the vacuum

D. The wavelength and electric-field direction

Answer: (B)

Explicación

In vacuum, the speed is c=1/√(μ₀ε₀), approximately 3×10⁸ m s⁻¹, so it is determined by vacuum permeability and permittivity.

16. An electromagnetic wave in vacuum has frequency 6.0×10¹⁴ Hz. What wavelength does it have approximately?

A. 5.0×10⁻⁷ m

B. 1.0×10⁻¹⁴ m

C. 1.8×10²³ m

D. 3.6×10⁸ m

Answer: (A)

Explicación

Using νλ=c, λ=c/ν=(3.0×10⁸)/(6.0×10¹⁴)=5.0×10⁻⁷ m.

17. How is the speed of an electromagnetic wave determined in a material with permittivity ε and permeability μ?

A. v=1/(με)

B. v=με

C. v=1/√(με)

D. v=√(με)

Answer: (C)

Explicación

In a material medium, the wave speed is v=1/√(με), so it depends on the medium's electromagnetic properties.

18. Which statement best describes the boundaries between neighboring regions of the electromagnetic spectrum?

A. They are determined solely by whether humans can detect the radiation

B. They are fixed by distinct sources that cannot produce adjacent regions

C. They are separated by gaps in which no electromagnetic waves exist

D. They are approximate and overlap rather than being sharply separated

Answer: (D)

Explicación

The spectrum is divided into approximate, overlapping bands, so adjacent regions do not have sharp boundaries.

19. What distinguishes electromagnetic waves in different regions of the spectrum when they travel through vacuum?

A. They have different speeds and different wavelengths

B. They have the same speed but different wavelengths and frequencies

C. They have the same wavelength but different speeds

D. They have different speeds but identical frequencies

Answer: (B)

Explicación

All electromagnetic waves travel at the same speed in vacuum, while their wavelengths and frequencies vary between spectrum regions.

20. How are radio waves used in communication systems, and what produces them?

A. They are produced by radioactive nuclei and used primarily for medical imaging

B. They are produced by hot bodies and used mainly in remote controls

C. They are produced by accelerated electrons in conducting wires and used for radio and television communication

D. They are produced by klystrons and used primarily in radar systems

Answer: (C)

Explicación

Accelerated electrons in conducting wires produce radio waves, which are used in radio and television communication systems. Klystrons are associated with microwave production rather than ordinary radio broadcasting.

21. A radar system requires electromagnetic radiation in the gigahertz frequency range. Which region and application are most appropriate?

A. Radio waves, because they are produced by accelerated electrons in conducting wires

B. Infrared waves, because they are emitted by hot bodies and absorbed by water molecules

C. Microwaves, because they are used in radar and can be produced by klystrons or magnetrons

D. Ultraviolet waves, because atmospheric ozone absorbs much of this radiation

Answer: (C)

Explicación

Microwaves occupy the gigahertz range and are used in radar; devices such as klystrons and magnetrons can produce them.

22. Which range most closely represents visible electromagnetic radiation and its detection?

A. Approximately 10¹⁶ to 10¹⁹ Hz, detected primarily by radioactive nuclei

B. Approximately 4×10¹⁴ to 7×10¹⁴ Hz, detected by the human eye

C. Approximately 10⁹ to 10¹² Hz, detected primarily by radar receivers

D. Approximately 10² to 10⁶ Hz, detected primarily by television antennas

Answer: (B)

Explicación

Visible rays have frequencies of roughly 4×10¹⁴ to 7×10¹⁴ Hz, corresponding to wavelengths of about 700 to 400 nm, and are detected by the human eye.

23. Which statement correctly characterizes gamma rays?

A. They have gigahertz frequencies and are produced mainly by Gunn diodes

B. They have very short wavelengths and are produced by nuclear reactions and radioactive nuclei

C. They have wavelengths of about 700 to 400 nm and are detected by the human eye

D. They are produced by molecular vibrations and are commonly used in remote controls

Answer: (B)

Explicación

Gamma rays have wavelengths from about 10⁻¹⁰ m to less than 10⁻¹⁴ m and originate from nuclear reactions and radioactive nuclei.