Question

The speed of electromagnetic waves in a medium depends on the ________.

• A. intensity of the wave
• B. initial phase of the wave
• C. permittivity and permeability of the medium
• D. energy it carries
• E. reflectivity of the medium

Hint:

In a vacuum, $c = \frac{1}{\sqrt{\mu_0\epsilon_0}} \approx 3 \times 10^8$ m/s.

Answer 1

The Correct Option is C

Step 1: Understanding the Concept
This question asks about the factors that determine the speed of electromagnetic (EM) waves, such as light, when they travel through a material medium (other than a vacuum).
Step 2: Key Formula or Approach
From Maxwell's equations, the speed of an electromagnetic wave (\(v\)) in a linear, isotropic, non-conducting medium is determined by the medium's electrical and magnetic properties: its electric permittivity (\(\epsilon\)) and magnetic permeability (\(\mu\)). The formula is:
\[ v = \frac{1}{\sqrt{\mu\epsilon}} \] In a vacuum, these properties are the permittivity of free space (\(\epsilon_0\)) and the permeability of free space (\(\mu_0\)), and the speed is the speed of light in vacuum, \(c\):
\[ c = \frac{1}{\sqrt{\mu_0\epsilon_0}} \] Step 3: Detailed Explanation
The formula \(v = \frac{1}{\sqrt{\mu\epsilon}}\) explicitly shows that the speed of an EM wave in a medium depends on the permeability (\(\mu\)) and permittivity (\(\epsilon\)) of that medium.
- Permittivity (\(\epsilon\)): A measure of how an electric field affects, and is affected by, a dielectric medium. It relates to the ability of the material to store electrical energy in an electric field.
- Permeability (\(\mu\)): A measure of the ability of a material to support the formation of a magnetic field within itself.
These two properties of the medium govern how the electric and magnetic fields of the wave propagate through it, thus determining the wave's speed.
Let's evaluate the options:
(A) intensity of the wave: The speed of light in a linear medium is independent of its intensity (brightness).
(B) initial phase of the wave: The phase is related to the starting point of the wave's cycle and does not affect its propagation speed.
(C) permittivity and permeability of the medium: Correct. These are the fundamental electrical and magnetic properties that determine the speed.
(D) energy it carries: The energy of an EM wave is related to its amplitude and frequency (\(E=h\nu\)), not its speed in a given medium.
(E) reflectivity of the medium: Reflectivity is a property of the interface between two media and determines how much of the wave is reflected, not the speed within the medium.
Step 4: Final Answer
The speed of electromagnetic waves in a medium depends on the permittivity and permeability of the medium.