Step 1: Understanding the Concept:
An electromagnetic (EM) wave consists of oscillating electric (\(E\)) and magnetic (\(B\)) fields that are perpendicular to each other and also perpendicular to the direction of wave propagation.
These fields are not independent; according to Maxwell's equations, a changing electric field generates a magnetic field, and a changing magnetic field generates an electric field.
In a vacuum, these waves travel at a constant speed, denoted by \(c\), which is approximately \(3 \times 10^{8}\) meters per second.
There is a fixed mathematical ratio between the strength (amplitude) of the electric field and the strength of the magnetic field at any point in space for a plane electromagnetic wave.
Step 2: Key Formula or Approach:
The fundamental relationship derived from Maxwell’s equations for electromagnetic waves in a vacuum is:
\[ c = \frac{E_{0}}{B_{0}} \]
Where:
\(E_{0}\) = Amplitude (peak value) of the electric field (measured in V/m or N/C)
\(B_{0}\) = Amplitude (peak value) of the magnetic field (measured in Tesla, T)
\(c\) = Speed of light in a vacuum
Step 3: Detailed Explanation:
The relation \(\frac{E_{0}}{B_{0}} = c\) implies that the electric field is numerically much larger than the magnetic field when measured in standard SI units.
For example, if the magnetic field amplitude is \(1 \times 10^{-6} \text{ T}\) (1 microTesla), the electric field amplitude would be:
\[ E_{0} = B_{0} \times c = (1 \times 10^{-6}) \times (3 \times 10^{8}) = 300 \text{ V/m} \]
This large difference in numerical value is due to the very high value of the speed of light.
However, interestingly, the energy density (energy per unit volume) contributed by the electric field is exactly equal to the energy density contributed by the magnetic field in an EM wave.
\[ u_{e} = \frac{1}{2} \epsilon_{0} E^{2} \text{ and } u_{m} = \frac{1}{2\mu_{0}} B^{2} \]
Using the relation \(c = \frac{1}{\sqrt{\mu_{0}\epsilon_{0}}}\) and \(E = cB\), one can prove that \(u_{e} = u_{m}\).
Since the question specifically asks for the name of the constant that represents the ratio of the amplitudes, the answer is "Speed of light."
This ratio holds true not just for amplitudes, but also for instantaneous values of the fields at any given moment in vacuum.
Step 4: Final Answer:
The ratio of electric field amplitudes to magnetic field amplitudes is equal to the speed of light.
Therefore, the correct option is (A).