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Summary

  • Electromagnetic waves carry momentum and exert radiation pressure.
  • The radiation pressure of an electromagnetic wave is directly proportional to its energy density.
  • The pressure is equal to twice the electromagnetic energy intensity if the wave is reflected and equal to the incident energy intensity if the wave is absorbed.

Conceptual questions

Why is the radiation pressure of an electromagnetic wave on a perfectly reflecting surface twice as large as the pressure on a perfectly absorbing surface?

The force on a surface acting over time Δ t is the momentum that the force would impart to the object. The momentum change of the light is doubled if the light is reflected back compared with when it is absorbed, so the force acting on the object is twice as great.

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

A Hubble Telescope photo of a comet. It appears as a bright dot with fuzzy light around it.
(credit: ESA, Hubble)
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(a) If the electric field and magnetic field in a sinusoidal plane wave were interchanged, in which direction relative to before would the energy propagate?
(b) What if the electric and the magnetic fields were both changed to their negatives?

a. According to the right hand rule, the direction of energy propagation would reverse. b. This would leave the vector S , and therefore the propagation direction, the same.

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Problems

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

1.99 × 10 −11 N/m 2

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What pressure does light emitted uniformly in all directions from a 100-W incandescent light bulb exert on a mirror at a distance of 3.0 m, if 2.6 W of the power is emitted as visible light?

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A microscopic spherical dust particle of radius 2 μm and mass 10 μg is moving in outer space at a constant speed of 30 cm/sec. A wave of light strikes it from the opposite direction of its motion and gets absorbed. Assuming the particle decelerates uniformly to zero speed in one second, what is the average electric field amplitude in the light?

F = m a = ( p ) ( π r 2 ) , p = m a π r 2 = ε 0 2 E 0 2 E 0 = 2 m a ε 0 π r 2 = 2 ( 10 −8 kg ) ( 0.30 m/s 2 ) ( 8.854 × 10 −12 C 2 / N · m 2 ) ( π ) ( 2 × 10 −6 m ) 2 E 0 = 7.34 × 10 6 V/m

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A Styrofoam spherical ball of radius 2 mm and mass 20 μg is to be suspended by the radiation pressure in a vacuum tube in a lab. How much intensity will be required if the light is completely absorbed the ball?

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Suppose that S avg for sunlight at a point on the surface of Earth is 900 W/m 2 . (a) If sunlight falls perpendicularly on a kite with a reflecting surface of area 0.75 m 2 , what is the average force on the kite due to radiation pressure? (b) How is your answer affected if the kite material is black and absorbs all sunlight?

a. 4.50 × 10 −6 N; b. it is reduced to half the pressure, 2.25 × 10 −6 N

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Sunlight reaches the ground with an intensity of about 1.0 kW/m 2 . A sunbather has a body surface area of 0.8 m 2 facing the sun while reclining on a beach chair on a clear day. (a) how much energy from direct sunlight reaches the sunbather’s skin per second? (b) What pressure does the sunlight exert if it is absorbed?

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Suppose a spherical particle of mass m and radius R in space absorbs light of intensity I for time t . (a) How much work does the radiation pressure do to accelerate the particle from rest in the given time it absorbs the light? (b) 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?

a. W = 1 2 π 2 r 4 m c 2 I 2 t 2 ; b . E = π r 2 I t

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Source:  OpenStax, University physics volume 2. OpenStax CNX. Oct 06, 2016 Download for free at http://cnx.org/content/col12074/1.3
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