32. Electromagnetic Waves

A radio transmitsa wave with intensity27.0 W/m²towardsaflat surface(perfectlyreflecting)witharea2m².Calculate the force and radiation pressure on the surface.

A powerful laser portrayed in a movie provides a 3-mm-diameter beam of green light with a power of 3 W. A good agent inside a spacecraft aims the laser beam at an enemy astronaut hovering outside. The mass of the enemy astronaut is 120 kg and the spacecraft 185,000 kg. (a) Determine the “radiation-pressure” force exerted on the enemy by the laser beam assuming her suit is perfectly reflecting. (b) If the enemy is 30 m from the spacecraft’s center of mass, estimate the gravitational force the spacecraft exerts on the enemy. (c) Which of the two forces is larger, and by what factor?

What is the maximum power level of a radio station so as to avoid electrical breakdown of air at a distance of 0.75 m from the transmitting antenna? Assume the antenna is a point source. Air breaks down in an electric field of about 3 x 10⁶ V/m.

The radiation pressure (Section 31–9) created by electromagnetic waves might someday be used to power spacecraft through the use of a “solar sail,” Example 31–8. (a) Assuming total reflection, what would be the pressure on a solar sail located at the same distance from the Sun as the Earth (where I = 1350 W/m²)? (b) Suppose the sail material has a mass density of 1 g/m². What would be the acceleration of the sail due to solar radiation pressure? (c) A realistic solar sail would have a payload. How big a sail would you need to accelerate a 100-kg payload at 1 x 10^-3 m/s²?

The intensity of sunlight reaching the earth is 1360 W/m². Assuming all the sunlight is absorbed, what is the radiation-pressure force on the earth? Give your answer in newtons.

A flashlight emits 2.8 W of light. As the light leaves the flashlight in one direction, a reaction force is exerted on the flashlight in the opposite direction. Estimate the size of this reaction force.

(II) Estimate the radiation pressure due to a bulb emitting 5.0 W of EM radiation on a highly absorbing surface at a distance of 8.0 cm from the center of the bulb. Estimate the force exerted on your fingertip if you place it at this point.

(II) Laser light can be focused (at best) to a spot with a radius r equal to its wavelength ⋋. Suppose a 1.0-W beam of green laser light (⋋ = 5 x 10^-7 m) forms such a spot and illuminates a cylindrical object of radius r and length r (Fig. 31–25). Estimate (a) the radiation pressure and force on the object, and (b) its acceleration, if its density equals that of water and it absorbs all the radiation. [This order-of-magnitude calculation convinced researchers of the feasibility of “optical tweezers,” page 916.]

For a science project, you would like to horizontally suspend an 8.5 by 11 inch sheet of black paper in a vertical beam of light whose dimensions exactly match the paper. If the mass of the sheet is 1.0 g, what light intensity will you need?