Describe the relationship of the radiation pressure and the energy thickness of one electromagnetic waveExplain how the radiation press of light, while small, can develop observable huge effects

Material objects consists of charged particles. One electromagnetic wave incident on the object exerts pressures on the fee particles, in accordance with the Lorentz force, (Figure). These forces do occupational on the corpuscle of the object, enhancing its energy, as disputed in the vault section. The energy that sunshine carries is a familiar part of every warm sunny day. A lot less acquainted feature the electromagnetic radiation is the incredibly weak push that electromagnetic radiation to produce by exerting a pressure in the direction of 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 understand the direction that the force for a very details case, consider a aircraft electromagnetic wave incident on a metal in i m sorry electron motion, as component of a current, is damped through the resistance the the metal, so the the median electron activity is in phase with the force causing it. This is equivalent to an item moving versus friction and stopping as shortly as the pressure pushing it stop ((Figure)). Once the electrical field is in the direction of the optimistic y-axis, electrons relocate in the an unfavorable y-direction, v the magnetic ar in the direction that the positive z-axis. By using the right-hand rule, and accountancy for the an adverse charge of the electron, we can see the the force on the electron indigenous the magnetic ar is in the direction that the hopeful x-axis, i m sorry is the direction of wave propagation. As soon as the E ar reverses, the B ar does too, and also the force is again in the very same direction. Maxwell’s equations in addition to the Lorentz force equation suggest the visibility of radiation push much an ext generally than this details example, however.

Electric and magnetic areas of an electromagnetic wave can combine to create a pressure in the direction the propagation, as illustrated for the special situation of electrons whose movement is extremely damped by the resistance of a metal.


The radiation pressure
used by one electromagnetic wave on a perfectly taking in surface turns out to be same to the energy thickness of the wave:


If the product is perfect reflecting, such together a steel surface, and if the incidence is along the typical to the surface, climate the press exerted is twice as much due to the fact that the momentum direction reverses ~ above reflection:


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(Figure) and (Figure) provide the instantaneous pressure, but due to the fact that the energy density oscillates rapidly, we are usually interested in the time-averaged radiation pressure, which can be composed in terms of intensity:

Radiation press plays a role in explaining plenty of observed astronomical phenomena, including the illustration of comets. Comets are basically chunks the icy product in i m sorry frozen gases and particles the rock and also dust room embedded. When a comet philosophies the Sun, that warms up and also its surface starts to evaporate. The coma of the comet is the hazy area around it indigenous the gases and also dust. Few of the gases and also dust kind tails once they leaving the comet. Notification in (Figure) that a comet has two tails. The ion tail (or gas tail in (Figure)) is composed mostly of ionized gases. This ions interact electromagnetically with the solar wind, i m sorry is a consistent stream of charged particles emitted by the Sun. The pressure of the solar wind top top the ionized gases is strong enough the the ion tail nearly always points directly away native the Sun. The second tail is written of dust particles. Because the dust tail is electrically neutral, that does not connect with the solar wind. However, this tail is influenced by the radiation pressure developed by the light from the Sun. Although fairly small, this push is solid enough to cause the dust tail to be displaced from the path of the comet.

Evaporation of material being warmed by the Sun forms two tails, as presented in this photograph of Comet Ison. (credit: modification of occupational by E. Slawik—ESO)
Halley’s Comet on February 9, 1986, Comet Halley to be at that closest suggest to the Sun, around
from the center of the Sun. The median power calculation of the sunlight is

(a) calculate the radiation pressure on the comet at this suggest in that orbit. Assume that the comet mirrors all the event light.

(b) intend that a 10-kg chunk of material of cross-sectional area

breaks loose from the comet. Calculate the force on this chunk due to the solar radiation. Compare this force with the gravitational force of the Sun.

Strategy calculation the strongness of solar radiation in ~ the provided distance indigenous the Sun and use that to calculation the radiation pressure. Native the pressure and area, calculate the force.


The pressure on the chunk due to the radiation is

Significance The gravitational pressure of the sunlight on the chunk is therefore much greater than the force of the radiation.

After Maxwell confirmed that light carried momentum and also energy, a novel idea eventually emerged, originally only as science fiction. Probably a spacecraft with a big reflecting irradiate sail can use radiation push for propulsion. Together a car would not have to lug fuel. That would suffer a continuous but little force indigenous solar radiation, instead of the short bursts from rocket propulsion. It would certainly accelerate slowly, yet by being accelerated continuously, it would ultimately reach an excellent speeds. A spacecraft with little total mass and also a sail through a huge area would be vital to achieve a usable acceleration.

When the space program began in the 1960s, the idea started to get serious fist from NASA. The many recent advancement in light thrust spacecraft has actually come native a citizen-funded group, the Planetary Society. It is currently testing the usage of light sails to propel a little vehicle constructed from CubeSats, small satellites the NASA areas in orbit for various research projects during room launches intended mostly for other purposes.

The LightSail spacecraft shown below ((Figure)) consists of 3 CubeSats bundled together. It has a full mass the only about 5 kg and also is about the size as a loaf of bread. Its sails are made of an extremely thin Mylar and also open ~ launch to have a surface ar area of


Two tiny CubeSat satellites deployed from the International an are Station in May, 2016. The solar sails open up out when the CubeSats space far enough away indigenous the Station. (credit: modification of work by NASA)
The an initial LightSail spacecraft was launched in 2015 to test the sail deployment system. The was put in low-earth orbit in 2015 by hitching a journey on one Atlas 5 rocket introduced for an unrelated mission. The test to be successful, but the low-earth orbit permitted too lot drag on the spacecraft to advice it through sunlight. Eventually, it burned in the atmosphere, as expected. The next Planetary Society’s LightSail solar cruising spacecraft is booked for 2016. One illustration the the spacecraft, as it is intended to show up in flight, can be seen on the Planetary Society’s website.

LightSail Acceleration The intensity of power from sunlight at a street of 1 AU indigenous the sun is

. The LightSail spacecraft has sails with total area that
and also a total mass of 5.0 kg. Calculation the best acceleration LightSail spacecraft could attain from radiation pressure as soon as it is around 1 AU from the Sun.

Strategy The maximum acceleration have the right to be expected as soon as the sail is opened straight facing the Sun. Use the irradiate intensity to calculation the radiation pressure and also from it, the force on the sails. Then usage Newton’s second law to calculation the acceleration.

Solution The radiation push is

Significance If this small acceleration continued for a year, the craft would acquire a speed of 1829 m/s, or 6600 km/h.

Check your Understanding just how would the speed and also acceleration of a radiation-propelled spacecraft be influenced as it relocated farther indigenous the sun on an interplanetary room flight?

Its acceleration would certainly decrease since the radiation force is proportional come the strongness of irradiate from the Sun, i beg your pardon decreases with distance. That speed, however, would not change except for the effects of gravity from the Sun and planets.


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

Why is the radiation pressure of an electromagnetic wave on a perfectly reflecting surface double as huge as the pressure on a perfectly soaking up surface?

The pressure on a surface ar acting over time

is the momentum that the pressure would send to the object. The momentum change of the light is double if the irradiate is reflected earlier compared with once it is absorbed, therefore the pressure acting top top the thing is twice as great.

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Why go the early Hubble Telescope picture of Comet Ison approaching Earth show it to have merely a fuzzy coma around it, and not the pronounced double tail that arisen later (see below)?

(credit: alteration of work by NASA, ESA, J.-Y. Li (Planetary science Institute), and also the Hubble Comet ISON Imaging scientific research Team)
(a) If the electric field and also magnetic field in a sinusoidal aircraft wave to be interchanged, in i m sorry direction loved one to prior to would the energy propagate? (b) What if the electric and also the magnetic fields were both changed to your negatives?

a. According to the best hand rule, the direction of power propagation would certainly reverse. B. This would leave the vector

, and also therefore the propagation direction, the same.

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

What press does irradiate emitted uniformly in all directions from a 100-W incandescence light pear exert top top a mirror at a distance of 3.0 m, if 2.6 W the the strength is emitted as visible light?

A microscope spherical dust bit of radius

and also mass
is relocating in outer an are at a continuous speed of 30 cm/sec. A wave of irradiate strikes the from the contrary direction that its motion and also gets absorbed. Presume the particle decelerates uniformly come zero rate in one second, what is the average electrical field amplitude in the light?

A Styrofoam spherical round of radius 2 mm and also mass

is to it is in suspended by the radiation pressure in a vacuum pipe in a lab. Just how much intensity will certainly be required if the light is totally absorbed the ball?

Suppose the

for sunlight at a point on the surface ar of earth is
. (a) If sunlight falls perpendicularly top top a kite v a mirroring surface that area
, what is the average force on the kite because of radiation pressure? (b) just how is your answer influenced if the kite material is black and also absorbs every sunlight?

Sunlight reaches the ground through an soot of about

. A sunbather has actually a body surface area of
facing the sun while reclining on a beach chair ~ above a clear day. (a) exactly how much power from straight sunlight get the sunbather’s skin every second? (b) What pressure does the sunshine exert if it is absorbed?

Suppose a spherical bit of fixed m and radius R in an are absorbs light of soot I for time t. (a) just how much occupational does the radiation pressure execute to accelerate the particle from rest in the given time that absorbs the light? (b) just how much energy carried by the electromagnetic waves is absorbed by the particle over this time based on the radiant energy incident on the particle?