∙∙A plane sinusoidal electromagnetic wave in air has a...

$\bullet$$\bullet$ A plane sinusoidal electromagnetic wave in air has a wave-length of 3.84 $\mathrm{cm}$ and an $\vec{\boldsymbol{E}}$ field amplitude of 1.35 $\mathrm{V} / \mathrm{m}$ . (a) What is the frequency of the wave? (b) What is the $\vec{\boldsymbol{B}}$ field amplitude? (c) What is the intensity? (d) What average force does this radiation exert perpendicular to its direction of propagation on a totally absorbing surface with area 0.240 $\mathrm{m}^{2}$ ?

$\bullet$$\bullet$ A plane sinusoidal electromagnetic wave in air has a wave-length of 3.84 $\mathrm{cm}$ and an $\vec{\boldsymbol{E}}$ field amplitude of 1.35 $\mathrm{V} / \mathrm{m}$ .
(a) What is the frequency of the wave? (b) What is the $\vec{\boldsymbol{B}}$ field amplitude? (c) What is the intensity? (d) What average force does this radiation exert perpendicular to its direction of propagation on a totally absorbing surface with area 0.240 $\mathrm{m}^{2}$ ?

Key Concepts

Electric and Magnetic Field Relationship

In an electromagnetic wave, the magnitudes of the electric field (E) and the magnetic field (B) are related by the speed of light (B = E/c). This relation arises from Maxwell’s equations in free space and is crucial for linking the two components of the wave’s oscillations. It ensures that the energy conveyed by the wave is consistently distributed between the two fields.

Intensity of Electromagnetic Waves

Intensity, often denoted by I, is defined as the power per unit area carried by a wave. For electromagnetic waves in free space, the intensity can be calculated using the relationship I = (1/2) c ?? E², where ?? is the permittivity of free space and E is the amplitude of the electric field. This concept is central in understanding how much energy is being transferred by the wave.

Wave Frequency Calculation

This concept involves using the fundamental relationship between the speed of a wave, its wavelength, and its frequency (v = ?f). For electromagnetic waves, the speed (v) in vacuum or air is a constant (c ? 3 x 10^8 m/s). This relation allows the determination of the frequency when the wavelength is known, and is one of the basic properties of all waves.

Radiation Pressure and Force

Radiation pressure is the pressure exerted by electromagnetic radiation on a surface due to the momentum carried by the photons. For a perfectly absorbing surface, the average radiation pressure is given by I/c. When multiplied by the surface area, this pressure yields the force exerted on the surface. This concept is important in contexts such as solar sails and optical trapping.

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