Questions & explanations
1. Which of the following correctly matches an electromagnetic radiation with its source and a common use?
- Visible light – emitted by radioactive decay; used in night vision devices
- Ultraviolet – emitted by hot bodies; used for remote sensing
- X-rays – produced when high-speed electrons strike a metal target; used for detecting fractures in bones
- Gamma rays – produced by electron transitions in atoms; used in cancer therapy
Answer: X-rays – produced when high-speed electrons strike a metal target; used for detecting fractures in bones
X-rays are generated when high-speed electrons are suddenly decelerated upon striking a metal target (bremsstrahlung) or by inner-shell electron transitions. They are commonly used in medical imaging to detect bone fractures. Visible light is not from radioactive decay; ultraviolet is primarily from the Sun and not typically from hot bodies for remote sensing; gamma rays originate from nuclear transitions, not electron transitions.
2. Which of the following is a correct source–use pair for the given electromagnetic radiation?
- Radio waves – from hot bodies; used in remote sensing
- Microwaves – from klystron valve; used in radar and oven
- Infrared – from accelerating charges; used for broadcasting
- Radio waves – from nuclear transitions; used in cancer treatment
Answer: Microwaves – from klystron valve; used in radar and oven
Microwaves are produced by klystron and magnetron valves and are widely used in radar systems and microwave ovens. Radio waves are produced by oscillating circuits, not hot bodies; infrared is produced by hot bodies and used in remote sensing, not by accelerating charges for broadcasting; radio waves are used for broadcasting, not for cancer treatment (that's gamma rays or X-rays).
3. The amplitudes of electric and magnetic fields in a plane electromagnetic wave are related as:
- E₀ = (1/√(μ₀ε₀)) B₀
- E₀ = √(μ₀/ε₀) B₀
- E₀ = (μ₀ε₀) B₀
- E₀ = (ε₀/μ₀) B₀
Answer: E₀ = (1/√(μ₀ε₀)) B₀
In a plane electromagnetic wave the peak electric and magnetic field amplitudes are related by E₀ = c B₀, where c is the speed of light. Since c = 1/√(μ₀ε₀), this is the same as E₀ = (1/√(μ₀ε₀)) B₀. The other choices give incorrect combinations: √(μ₀/ε₀) is the impedance of free space, while (μ₀ε₀) and (ε₀/μ₀) do not have the correct units or value.
4. To establish continuity of current in a circuit containing a capacitor, Maxwell introduced a term called displacement current in the Ampere-Maxwell law. The displacement current is due to:
- Conduction current flowing through the capacitor plates
- Time-varying electric field between the capacitor plates
- Time-varying magnetic field between the capacitor plates
- Movement of free electrons between the capacitor plates
Answer: Time-varying electric field between the capacitor plates
Displacement current arises from a time-varying electric field, as given by the term ε₀(dΦₑ/dt) in the Ampere-Maxwell law. Between capacitor plates during charging/discharging, the changing electric field produces displacement current ensuring continuity of current, even though no conduction current flows across the gap.
5. According to Maxwell's equations, which of the following correctly describes a fundamental symmetry in electromagnetism?
- A steady electric field produces a magnetic field
- A changing electric field produces a magnetic field
- A steady magnetic field produces an electric field
- A changing magnetic field produces a constant electric field
Answer: A changing electric field produces a magnetic field
Maxwell's equations state that a time-varying electric field generates a magnetic field (via displacement current), and a time-varying magnetic field generates an electric field (via Faraday’s law). This symmetry is essential for the existence of electromagnetic waves.
6. Arrange the following electromagnetic radiations in order of increasing frequency:
- Radio waves, Microwaves, Infrared, Visible
- Visible, Infrared, Microwaves, Radio waves
- Infrared, Visible, Ultraviolet, Radio waves
- Gamma rays, X-rays, Ultraviolet, Visible
Answer: Radio waves, Microwaves, Infrared, Visible
The electromagnetic spectrum in order of increasing frequency (or decreasing wavelength) is: Radio waves, Microwaves, Infrared, Visible, Ultraviolet, X-rays, Gamma rays. Option A correctly places radio waves at lowest frequency and visible at higher frequency.
7. The speed of electromagnetic waves in free space is given by c = 1/√(μ₀ε₀). This expression implies that the speed of EM waves in vacuum depends on:
- The electric and magnetic fields of the wave
- The frequency and wavelength of the wave
- The permittivity and permeability of free space
- The amount of charge producing the wave
Answer: The permittivity and permeability of free space
Maxwell derived that electromagnetic waves travel at speed c = 1/√(μ₀ε₀), where μ₀ is the permeability of free space and ε₀ is the permittivity of free space. This is a constant independent of field amplitudes, frequency, or source details.
8. In a plane electromagnetic wave propagating along the z-direction, the electric field vector is along the x-axis. The magnetic field vector will be along:
- x-axis
- y-axis
- z-axis
- Negative x-axis
Answer: y-axis
For an EM wave, the electric field (E), magnetic field (B), and propagation direction (k̂) are mutually perpendicular. If propagation is along z and E is along x, then B must be along y (since E × B gives the direction of propagation).
9. Electromagnetic waves are transverse in nature because:
- The electric and magnetic fields oscillate in the direction of propagation
- The electric field oscillates parallel to the magnetic field
- Both electric and magnetic fields oscillate perpendicular to the direction of wave propagation
- The wave propagates only in vacuum
Answer: Both electric and magnetic fields oscillate perpendicular to the direction of wave propagation
In an electromagnetic wave, the oscillating electric field (E) and magnetic field (B) are mutually perpendicular to each other and also perpendicular to the direction of propagation, which is the defining property of transverse waves.