The magnetic field in a radio wave traveling through air has...

The magnetic field in a radio wave traveling through air has amplitude $2.5 \times 10^{-11} \mathrm{T}$ and frequency $3.0 \mathrm{MHz}$ (a) Find the amplitude and frequency of the electric field. (b) The wave is traveling in the $-y$ -direction. At $y=0$ and $t=0,$ the magnetic field is $1.5 \times 10^{-11} \mathrm{T}$ in the +z-direction. What are the magnitude and direction of the electric field at $y=0$ and $t=0 ?$

The magnetic field in a radio wave traveling through air has amplitude $2.5 \times 10^{-11} \mathrm{T}$ and frequency $3.0 \mathrm{MHz}$
(a) Find the amplitude and frequency of the electric field.
(b) The wave is traveling in the $-y$ -direction. At $y=0$ and $t=0,$ the magnetic field is $1.5 \times 10^{-11} \mathrm{T}$ in the +z-direction. What are the magnitude and direction of the electric field at $y=0$ and $t=0 ?$

Key Concepts

Electromagnetic Waves

Electromagnetic waves are oscillations of electric and magnetic fields that propagate through space. These waves are solutions to Maxwell's equations and are characterized by their frequency, wavelength, and amplitude. In a vacuum or in air, electromagnetic waves travel at the speed of light, and both the electric and magnetic fields oscillate sinusoidally and are perpendicular to each other and to the direction of propagation.

Relationship Between Electric and Magnetic Fields

In electromagnetic waves traveling in free space, the magnitudes of the electric and magnetic fields are directly related by the speed of light (c), following the relation E = cB. This means that if the magnetic field amplitude is known, the electric field amplitude can be calculated by multiplying the magnetic field amplitude by the speed of light. Additionally, both fields share the same frequency and are in phase in a plane wave.

Right-Hand Rule and Field Orientation

For electromagnetic waves, the directions of the electric field, magnetic field, and the wave’s propagation are mutually perpendicular. The right-hand rule is used to determine these directions: pointing the index finger in the direction of the electric field and the middle finger in the direction of the magnetic field, the thumb then points in the direction of wave propagation. This rule is essential for understanding the spatial orientation and phase relationships of the fields in a propagating electromagnetic wave.

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