Home » Civil Engineering » Elements of Remote Sensing

Energy carried by an electromagnetic (EM) wave — dependence on amplitude In wave physics and remote sensing, the time-averaged transported energy (intensity) of an EM wave is directly related to the field amplitude. Choose the correct proportionality between transported energy and wave amplitude.

Difficulty: Easy

proportional to the amplitude
proportional to the square of the amplitude
proportional to the cube of the amplitude
proportional to the square root of the amplitude
None of these

Correct Answer: proportional to the square of the amplitude

Explanation:

Introduction / Context:
The energy flow in an electromagnetic (EM) wave is described by the Poynting vector. For sinusoidal waves, the time-averaged magnitude (intensity) depends on the amplitudes of the electric and magnetic fields. This question checks whether you know the correct amplitude–energy relationship used throughout optics, antennas, and remote sensing radiometry.

Given Data / Assumptions:

Plane monochromatic EM wave in a linear, isotropic, non-magnetic medium (air approximation).
Electric field peak amplitude E0; magnetic field peak amplitude H0.
We compare how the transported energy varies with amplitude.

Concept / Approach:
Instantaneous Poynting vector S = E × H. For harmonic waves, the time-average intensity I = is proportional to the product of field amplitudes. Since H0 is proportional to E0 in a given medium, intensity scales as E0^2. Thus, transported energy per unit area per unit time varies with the square of amplitude.

~~Step-by-Step Solution:~~

1) Write S = E × H; magnitude S = E * H for orthogonal fields.2) In a non-magnetic medium, H0 = E0 / η, where η is wave impedance.3) Therefore, I ∝ E0 * (E0 / η) = (1/η) * E0^2 ⇒ intensity ∝ amplitude^2.4) Hence, transported energy is proportional to the square of the amplitude.

Verification / Alternative check:
Optical irradiance from a source falls off with distance but, at a given point, doubling field amplitude quadruples intensity, consistent with photodetector response in the linear regime.

Why Other Options Are Wrong:
Proportional to amplitude / square root / cube: incorrect scaling; the correct is square.
None of these: Not true because square-law dependence is standard.

Common Pitfalls:
Confusing field amplitude with power; forgetting that many detectors and link budgets use the square-law relation for EM waves.

Final Answer:
proportional to the square of the amplitude

← Previous Question Next Question→

More Questions from Elements of Remote Sensing

Electromagnetic spectrum facts — wavelengths and the visible window Pick the correct combined statement about gamma-ray wavelengths, radio-wave wavelengths, and the visible band extent used in remote sensing.

Solar radiation through the atmosphere — identify the incorrect statement As solar radiation traverses the atmosphere it may be scattered and absorbed. Which statement below is incorrect?

Dielectric properties and relative permittivity — pick the correct statement(s) Consider relative permittivity (dielectric constant) and its implications. Which combined statement is correct?

Remote sensing basics — signature, reflectance, and Lambertian surfaces Choose the comprehensive correct statement set about object signatures, reflectance definition, and Lambertian behaviour in remote sensing.

GIS capabilities versus traditional mapping — identify the incorrect statement Which statement about Geographic Information Systems (GIS) is NOT correct?

Ocean colour — appearance of waters poor in phytoplankton under sunlight In clear open-ocean conditions with low phytoplankton concentration, what colour does the water typically appear to the human eye?

GPS ranging signals — operational L-band frequencies The standard GPS system performs code and carrier ranging using how many L-band frequencies?

Structure of an electromagnetic wave — fields, orientation, and polarisation Pick the comprehensive correct statement set about the composition of EM waves, field orientation, and the meaning of polarisation.

Vegetation canopy optics — region with maximum multiple-leaf effect In which part of the reflective optical/infrared spectrum is the effect of multiple leaves in a vegetation canopy (strong internal scattering) most pronounced?

Snow Optics – Spectral reflectance behaviour of fresh, pure snow In remote sensing of cryosphere, how does the reflectance of fresh and pure snow vary across the spectrum (visible, near-IR, and longer wavelengths)?

Discussion & Comments

No comments yet. Be the first to comment!

Posting…

Name

Comment

Join Discussion