The electric field in a radio wave traveling through vacuum...

The electric field in a radio wave traveling through vacuum has amplitude $2.5 \times 10^{-4} \mathrm{V} / \mathrm{m}$ and frequency $1.47 \mathrm{MHz}$. (a) Find the amplitude and frequency of the magnetic field. (b) The wave is traveling in the $+x$ -direction. At $x=0$ and $t=0,$ the electric field is $1.5 \times 10^{-4} \mathrm{V} / \mathrm{m}$ in the - y-direction. What are the magnitude and direction of the magnetic field at $x=0$ and $t=0 ?$.

The electric field in a radio wave traveling through vacuum has amplitude $2.5 \times 10^{-4} \mathrm{V} / \mathrm{m}$ and frequency $1.47 \mathrm{MHz}$.
(a) Find the amplitude and frequency of the magnetic field. (b) The wave is traveling in the $+x$ -direction. At $x=0$ and $t=0,$ the electric field is $1.5 \times 10^{-4} \mathrm{V} / \mathrm{m}$ in the
- y-direction. What are the magnitude and direction of the magnetic field at $x=0$ and $t=0 ?$.

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Key Concepts

Wave Frequency Consistency

The frequency of an electromagnetic wave is a fundamental property and remains the same for both the electric and magnetic components. This constant frequency signifies that the oscillations of the electric and magnetic fields are synchronized, and it directly influences other wave characteristics such as energy and wavelength.

Electromagnetic Waves

Electromagnetic waves are oscillations of electric and magnetic fields that propagate through space. In a vacuum, these fields travel at the speed of light and are oriented perpendicular to one another as well as to the direction of propagation. This underlying framework is provided by Maxwell's equations, which dictate the behavior and interdependence of the fields.

Relationship Between Electric and Magnetic Fields

In vacuum, there exists a direct proportionality between the amplitudes of the electric field (E) and the magnetic field (B), which is given by the equation E = cB, where c is the speed of light. This relationship not only links the magnitudes of these fields but also reflects their phase coherence and mutual orientation, ensuring that both fields oscillate in synchrony within the electromagnetic wave.

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