33.11
Momentum And Radiation Pressure
An object absorbing an electromagnetic wave would experience a force in the direction of propagation of the wave. This force occurs because electromag…
Electromagnetic waves transport momentum while traveling through space. The corresponding momentum density is expressed in terms of the Poynting vector magnitude and the speed of light.
By substituting the volume occupied by the wave that passes through an area in a short interval of time, the momentum flow rate per unit area can be obtained.
The average rate of momentum transfer per unit area is obtained by replacing the average value of the Poynting vector with intensity.
Due to the transfer of momentum, electromagnetic waves exert pressure on the surface, known as radiation pressure.
Now, the average rate of change of momentum equals average force and force per unit area is the radiation pressure.
Thus, the radiation pressure is directly proportional to the intensity of the wave.
If the surface perfectly absorbs the electromagnetic wave, the corresponding momentum is also transferred completely to the surface.
For a perfectly reflecting surface, the momentum change will be double. Thus, the radiation pressure also doubles.
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Q1: How do electromagnetic waves carry and transport momentum?
Electromagnetic waves transport momentum while traveling through space, with momentum density expressed in terms of the Poynting vector magnitude and the speed of light. By calculating the volume of the wave passing through an area in a short time interval, the momentum flow rate per unit area can be determined. This momentum transport is fundamental to understanding how waves exert forces on surfaces.
Q2: What is radiation pressure and how does it relate to wave intensity?
Radiation pressure is the force per unit area exerted by electromagnetic waves on a surface due to momentum transfer. The average rate of momentum transfer per unit area equals the radiation pressure, which is directly proportional to the intensity of the wave. Using intensity instead of the Poynting vector provides a practical way to calculate radiation pressure on surfaces.
Q3: Why does radiation pressure differ between absorbing and reflecting surfaces?
For a perfectly absorbing surface, all momentum from the electromagnetic wave transfers completely to the surface, creating a baseline radiation pressure equal to the wave's energy density. For a perfectly reflecting surface, the momentum direction reverses upon reflection, causing the momentum change to double. Consequently, radiation pressure on a reflecting surface is twice that on an absorbing surface.
Q4: How was radiation pressure experimentally confirmed?
Maxwell's prediction of radiation pressure was confirmed in 1903 by Nichols and Hull using a torsion balance with suspended mirrors inside a glass container. When light shone on one mirror, they measured a slight but measurable deflection. From this deflection, they calculated the unbalanced force on the mirror and obtained agreement with the theoretically predicted force value.
Q5: How does radiation pressure affect comet tails?
Comets develop two types of tails when approaching the Sun. The ion tail, composed of ionized gases, interacts with the solar wind and points away from the Sun. The dust tail, electrically neutral and unaffected by the solar wind, is displaced by radiation pressure from sunlight. Although relatively small, this pressure is strong enough to cause the dust tail to deviate from the comet's path.
Q6: What is the relationship between momentum flow rate and radiation pressure?
The average rate of change of momentum equals average force, and force per unit area defines radiation pressure. By replacing the average Poynting vector value with intensity, the momentum flow rate per unit area can be expressed as radiation pressure. This relationship shows that radiation pressure is a direct consequence of momentum transfer from electromagnetic waves to surfaces.
Q7: How does the Poynting vector relate to calculating radiation pressure?
The Poynting vector magnitude expresses momentum density in electromagnetic waves. By substituting the volume occupied by the wave passing through an area in a short time interval, the momentum flow rate per unit area can be obtained. This calculation forms the basis for determining radiation pressure before simplifying the expression using intensity values.