Radiation Pressure A plane electromagnetic wave, with...

Radiation Pressure A plane electromagnetic wave, with wavelength $3.0 \mathrm{m},$ travels in vacuum in the positive direction of an $x$ axis. The electric field, of amplitude $300 \mathrm{V} / \mathrm{m},$ oscillates parallel to the $y$ axis. What are the (a) frequency, (b) angular frequency, and (c) angular wave number of the wave? (d) What is the amplitude of the magnetic field component? (e) Parallel to which axis does the magnetic field oscillate? (f) What is the time-averaged rate of energy flow in watts per square meter associated with this wave? The wave uniformly illuminates a surface of area 2.0 $\mathrm{m}^{2} .$ If the surface totally absorbs the wave, what are (g) the rate at which momentum is transferred to the surface and ( h the radiation pressure on the surface?

Radiation Pressure
A plane electromagnetic wave, with wavelength $3.0 \mathrm{m},$ travels in vacuum in the positive direction of an $x$ axis. The electric field, of amplitude $300 \mathrm{V} / \mathrm{m},$ oscillates parallel to the $y$ axis. What are the (a) frequency, (b) angular frequency, and (c) angular wave number of the wave? (d) What is the amplitude of the magnetic field component? (e) Parallel to which axis does the magnetic field oscillate? (f) What is the time-averaged rate of energy flow in watts per square meter associated with this wave? The wave uniformly illuminates a surface of area 2.0 $\mathrm{m}^{2} .$ If the surface totally absorbs the wave, what are (g) the rate at which momentum is transferred to the surface and ( h the radiation pressure on the surface?

Key Concepts

Radiation Pressure and Momentum Transfer

Radiation pressure is the pressure exerted upon any surface due to the momentum carried by electromagnetic waves. It arises because energy and momentum are transferred when the wave interacts with matter, and for a totally absorbing surface, the pressure can be derived from the incident intensity divided by the speed of light.

Poynting Vector and Energy Flux

The Poynting vector represents the rate at which energy is transferred per unit area by an electromagnetic wave, often interpreted as the energy flux or intensity. Its magnitude depends on the amplitudes of the electric and magnetic fields and includes factors from the vacuum permittivity and the speed of light.

Electric and Magnetic Field Relationship in a Plane Wave

In electromagnetic plane waves propagating in vacuum, the amplitudes of the electric and magnetic fields are related by the speed of light; specifically, the magnetic field amplitude is the electric field amplitude divided by the speed of light. This relationship stems from Maxwell's equations.

Wavelength and Angular Wave Number

Wavelength is the distance between successive peaks of a wave, while the angular wave number represents the spatial frequency of the wave and is calculated by dividing 2? by the wavelength. This concept helps describe how the wave oscillates in space.

Frequency and Angular Frequency

Frequency is the number of oscillations per unit time, and angular frequency is the rate of change of the waveform's phase expressed in radians per second. The two are related by the factor 2?, with angular frequency equal to 2? times the frequency.

Electromagnetic Wave Propagation

This concept describes the behavior of electromagnetic waves traveling through space, especially in a vacuum. It includes understanding that such waves consist of oscillating electric and magnetic fields that are perpendicular to each other and to the direction of propagation, and that they travel at the speed of light in vacuum.

Transcript

00:01 So in this situation here, and they give you a electromagnetic wave and want to know the frequency, angular frequency, angular wave number of the wave, and then some information about the magnetic field.

00:15 So let's work out each step.

00:17 So the information of the electromagnetic wave is here.

00:21 So it is traveling to the x direction and the electromagnetic theory oscillating parallel to the y.

00:28 With this magnitude and this wavelength.

00:31 So first they want to know the frequency of the wave.

00:35 So a frequency because the wave travels at the speed of life is c over lambda.

00:45 And we can just substitute the value here.

00:48 2 .998 times 10 to the 8 divided by 3 .0.

00:59 This is everything emitters.

01:01 This gives us 1 .0 times 10 to the 8.

01:05 8 hertz.

01:09 Now from f we can find the angular frequency that they want for b.

01:14 So the angular frequency is just 2 pi times f and this is just 2 pi 1 .0 times 10 to the 8.

01:29 And this gives us 6 .3 times 10 to the 8 radiance per second.

01:41 Now they want to know the way the wave number also can find directly from the wavelength.

01:48 So the wave number, k, is 2 pi divided by lambda.

01:57 So this is just 2 pi divided by 3 meters.

02:03 And it is 2 .1 radiance divided by meters.

02:10 Now the second part, they want to know what is the amplitude of the magnetic field component...

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