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Electromagnetic waves are fascinating and can be characterized by both electric and magnetic fields that oscillate in harmony. In any electromagnetic wave traveling through a vacuum, the electric field (\( E \)) is interlinked with the magnetic field (\( B \)) through the simple and fundamental relationship: \[ E = cB \]This equation tells us that the magnitude of the electric field is equal to the speed of light (\( c = 3.00 \times 10^8 \text{ m/s} \)) multiplied by the magnitude of the magnetic field.

In a given problem, if we know the magnetic field amplitude is \( 5.80 \times 10^{-4} \text{ T} \), the electric field's magnitude can be calculated by inputting these values into the formula:

• Given: \( B = 5.80 \times 10^{-4} \text{ T} \)
• Use: \( E = cB \)
• Calculation: \( E = (3.00 \times 10^8 \text{ m/s})(5.80 \times 10^{-4} \text{ T}) = 1.74 \times 10^5 \text{ V/m} \)

We conclude that the electric field's magnitude is \( 1.74 \times 10^5 \text{ V/m} \). This formula is incredibly useful for connecting the electric and magnetic aspects of electromagnetic waves.

Magnetic fields in electromagnetic waves are just as crucial as electric fields, having their own amplitude and direction. Such fields are oriented perpendicular to both the electric field and the direction of wave propagation.

In our specific problem, the magnetic field is oriented parallel to the y-axis while the wave propagates in the +x direction. This orientation is essential, as it dictates the direction of the electric field to ensure that all components maintain perpendicular alignment:

• The magnetic field's amplitude is given as \( 5.80 \times 10^{-4} \text{ T} \)
• It follows the equation for wave functions: \( B(x, t) = B_0 \sin(kx - \omega t) \)

This sin function allows us to describe the oscillating nature of the magnetic field as the wave moves through space and time, with \( B_0 \) representing the wave’s maximum magnetic field strength. By understanding these core principles, we can comprehend the dynamic and interconnected relationship between electric and magnetic fields in electromagnetic waves.

The wave function is a mathematical representation that describes how electromagnetic waves vary in space and time. Both the electric and magnetic components of an electromagnetic wave can be expressed through wave functions, typically presented in sinusoidal forms.

For an electromagnetic wave traveling in the +x direction with a frequency of \( 6.10 \times 10^{14} \text{ Hz} \), we use the wave function formula to describe the electric field component. This is noted as:\[ E(x, t) = E_0 \sin(kx - \omega t) \]where:

• \( E_0 \) is the amplitude of the electric field, \( 1.74 \times 10^5 \text{ V/m} \)
• \( k \) is the wave number, calculated as \( k = \frac{\omega}{c} \) with \( \omega \) being the angular frequency \( 2\pi f \)
• \( \omega \) is \( 2\pi \times 6.10 \times 10^{14} \)

Similarly for the magnetic field:\[ B(x, t) = B_0 \sin(kx - \omega t) \]where \( B_0 \) is the magnetic field amplitude. These equations mirror the sinusoidal nature of wave propagation and provide valuable insights into how waves behave over time and across distances, presenting a full picture of the oscillating fields within an electromagnetic wave.