Describe the connection of the radiation pressure and the energy density of one electromagnetic waveExplain just how the radiation push of light, if small, can develop observable expensive effects

Material objects consist of charged particles. An electromagnetic wave event on the object exerts forces on the charged particles, in accordance with the Lorentz force, (Figure). These forces do job-related on the corpuscle of the object, raising its energy, as questioned in the previous section. The power that sunlight carries is a familiar component of every heat sunny day. A much less familiar feature that electromagnetic radiation is the incredibly weak push that electromagnetic radiation to produce by exerting a pressure in the direction that the wave. This force occurs due to the fact that electromagnetic waves contain and also transport momentum.

You are watching: Find the average momentum density (momentum per unit volume) in the light at the floor.

To recognize the direction of the force for a very particular case, take into consideration a plane electromagnetic wave event on a metal in i beg your pardon electron motion, as component of a current, is damped through the resistance of the metal, so the the median electron motion is in phase through the pressure causing it. This is equivalent to an item moving versus friction and also stopping as soon as the force pushing it stops ((Figure)). As soon as the electrical field is in the direction that the confident y-axis, electrons move in the negative y-direction, with the magnetic field in the direction the the optimistic z-axis. By using the right-hand rule, and accounting for the an adverse charge the the electron, we have the right to see that the pressure on the electron indigenous the magnetic ar is in the direction that the positive x-axis, i m sorry is the direction of tide propagation. As soon as the E ar reverses, the B field does too, and the force is again in the same direction. Maxwell’s equations along with the Lorentz force equation indicate the existence of radiation pressure much more generally than this particular example, however.

Electric and also magnetic areas of one electromagnetic tide can combine to develop a pressure in the direction that propagation, as shown for the special case of electrons whose movement is very damped by the resistance the a metal.


The radiation press
applied by an electromagnetic tide on a perfectly absorbing surface transforms out come be same to the energy density of the wave:


If the material is perfectly reflecting, such as a steel surface, and if the incidence is follow me the typical to the surface, climate the press exerted is double as much because the inert direction reverses top top reflection:


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(Figure) and also (Figure) give the instantaneous pressure, but because the energy thickness oscillates rapidly, we are usually interested in the time-averaged radiation pressure, which deserve to be created in terms of intensity:

Radiation push plays a role in explaining countless observed huge phenomena, including the illustration of comets. Comets are basically chunks the icy material in which frozen gases and also particles that rock and also dust are embedded. As soon as a comet approaches the Sun, that warms up and its surface begins to evaporate. The coma that the comet is the hazy area roughly it from the gases and also dust. Some of the gases and also dust form tails as soon as they leave the comet. Notification in (Figure) the a comet has actually two tails. The ion tail (or gas tail in (Figure)) is composed largely of ionized gases. This ions interact electromagnetically v the solar wind, i m sorry is a continuous stream of fee particles emitted by the Sun. The pressure of the solar wind ~ above the ionized gases is solid enough that the ion tail practically always points straight away native the Sun. The 2nd tail is created of dust particles. Because the dust tail is electrically neutral, the does not interact with the solar wind. However, this tail is impacted by the radiation pressure created by the light from the Sun. Although fairly small, this press is strong enough to cause the dust tail to be displaced indigenous the route of the comet.

Evaporation of material being warmed by the Sun develops two tails, as displayed in this photo of Comet Ison. (credit: change of occupational by E. Slawik—ESO)
Halley’s Comet top top February 9, 1986, Comet Halley was at that is closest point to the Sun, about
indigenous the center of the Sun. The average power calculation of the sunlight is

(a) calculate the radiation press on the comet at this point in that is orbit. Assume the the comet reflects all the incident light.

(b) mean that a 10-kg chunk of product of cross-sectional area

breaks loosened from the comet. Calculate the pressure on this chunk because of the solar radiation. Compare this pressure with the gravitational force of the Sun.

Strategy calculate the soot of solar radiation at the provided distance from the Sun and use the to calculate the radiation pressure. Indigenous the pressure and area, calculate the force.


The pressure on the chunk due to the radiation is

Significance The gravitational pressure of the sun on the chunk is thus much higher than the pressure of the radiation.

After Maxwell confirmed that light lugged momentum as well as energy, a novel idea at some point emerged, initially only as science fiction. Maybe a spacecraft v a large reflecting irradiate sail might use radiation pressure for propulsion. Such a vehicle would not have actually to bring fuel. That would endure a consistent but little force from solar radiation, rather of the brief bursts indigenous rocket propulsion. It would accelerate slowly, yet by being increased continuously, it would eventually reach good speeds. A spacecraft with tiny total mass and a sail v a large area would certainly be crucial to achieve a usable acceleration.

When the an are program began in the 1960s, the idea started to get serious fist from NASA. The many recent advancement in light propelled spacecraft has actually come indigenous a citizen-funded group, the Planetary Society. That is at this time testing the use of irradiate sails to propel a small vehicle built from CubeSats, small satellites that NASA places in orbit for various research jobs during room launches intended greatly for other purposes.

The LightSail spacecraft shown below ((Figure)) consists of three CubeSats bundled together. It has actually a full mass that only around 5 kg and is around the dimension as a bread of bread. The sails room made of an extremely thin Mylar and also open after ~ launch to have actually a surface area that


Two tiny CubeSat satellites deployed indigenous the International space Station in May, 2016. The solar sails open up out as soon as the CubeSats are far enough away indigenous the Station. (credit: change of work by NASA)
The an initial LightSail spacecraft was released in 2015 to test the sail deployment system. It was inserted in low-earth orbit in 2015 by hitching a journey on one Atlas 5 rocket released for one unrelated mission. The test to be successful, however the low-earth orbit permitted too much drag ~ above the spacecraft to accelerate it by sunlight. Eventually, it burned in the atmosphere, together expected. The following Planetary Society’s LightSail solar cruising spacecraft is reserved for 2016. One illustration the the spacecraft, as it is meant to appear in flight, can be seen on the Planetary Society’s website.

LightSail Acceleration The strongness of energy from sunshine at a street of 1 AU native the sun is

. The LightSail spacecraft has actually sails with complete area that
and also a total mass that 5.0 kg. Calculation the maximum acceleration LightSail spacecraft could accomplish from radiation pressure as soon as it is about 1 AU from the Sun.

Strategy The best acceleration can be expected once the sail is opened straight facing the Sun. Usage the light intensity to calculate the radiation pressure and also from it, the force on the sails. Then usage Newton’s 2nd law to calculate the acceleration.

Solution The radiation press is

Significance If this little acceleration ongoing for a year, the craft would attain a speed of 1829 m/s, or 6600 km/h.

Check her Understanding exactly how would the speed and also acceleration that a radiation-propelled spacecraft be impacted as it relocated farther indigenous the sun on an interplanetary room flight?

Its acceleration would decrease since the radiation pressure is proportional to the soot of light from the Sun, i m sorry decreases v distance. The speed, however, would certainly not adjust except because that the effects of heaviness from the Sun and planets.


Electromagnetic waves carry momentum and exert radiation pressure.The radiation pressure of an electromagnetic tide is straight proportional come its power density.The push is equal to double the electromagnetic energy intensity if the tide is reflected and equal to the incident energy intensity if the tide is absorbed.

Why is the radiation press of an electromagnetic tide on a perfectly reflecting surface double as large as the press on a perfectly taking in surface?

The pressure on a surface acting with time

is the momentum the the pressure would impart to the object. The momentum readjust of the light is doubled if the irradiate is reflected back compared with as soon as it is absorbed, for this reason the pressure acting ~ above the object is twice as great.

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Why walk the at an early stage Hubble Telescope photos of Comet Ison approaching Earth present it to have actually merely a fuzzy coma about it, and also not the pronounced dual tail that arisen later (see below)?

(credit: change of work by NASA, ESA, J.-Y. Li (Planetary scientific research Institute), and also the Hubble Comet ISON Imaging scientific research Team)
(a) If the electric field and also magnetic field in a sinusoidal plane wave to be interchanged, in i beg your pardon direction relative to before would the energy propagate? (b) What if the electric and the magnetic fields were both changed to your negatives?

a. Follow to the ideal hand rule, the direction of energy propagation would certainly reverse. B. This would leave the vector

, and therefore the propagation direction, the same.

A 150-W lightbulb emits 5% the its power as electromagnetic radiation. What is the radiation push on an absorbing sphere of radius 10 m that surrounds the bulb?

What push does light emitted uniformly in every directions from a 100-W incandescent light pear exert ~ above a mirror at a distance of 3.0 m, if 2.6 W the the power is emitted together visible light?

A microscopic spherical dust fragment of radius

and mass
is moving in outer space at a continuous speed that 30 cm/sec. A wave of light strikes it from the opposite direction that its motion and also gets absorbed. Presume the fragment decelerates uniformly to zero rate in one second, what is the average electric field amplitude in the light?

A Styrofoam spherical ball of radius 2 mm and mass

is to it is in suspended by the radiation push in a vacuum pipe in a lab. Just how much intensity will be forced if the light is fully absorbed the ball?

Suppose that

for sunlight at a point on the surface ar of earth is
. (a) If sunlight falls perpendicularly on a kite through a showing surface the area
, what is the average pressure on the kite because of radiation pressure? (b) how is your answer influenced if the kite product is black and absorbs all sunlight?

Sunlight get the ground with an soot of around

. A sunbather has a body surface area that
facing the sun while reclining on a coast chair top top a clear day. (a) just how much energy from direct sunlight get the sunbather’s skin every second? (b) What pressure does the sunshine exert if the is absorbed?

Suppose a spherical fragment of massive m and radius R in an are absorbs light of intensity I for time t. (a) exactly how much job-related does the radiation pressure do to advice the bit from rest in the provided time it absorbs the light? (b) exactly how much energy carried by the electromagnetic waves is took in by the particle over this time based on the radiant energy incident on the particle?