The microwave radiation left over from the Big Bang explosion of the universe has an average energy density of 3.81 × 10-14 J/m³. What is the rms value of the electric field of this radiation? Number i Units
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- CASE STUDY In Example 34.6 (page 1111), we imagined equipping 1950DA, an asteroid on a collision course with the Earth, with a solar sail in hopes of ejecting it from the solar system. We found that the enormous size required for the solar sail makes the plan impossible at this time. Of course, there is no need to eject such an object from the solar system: we only need to change the orbit. A much more pressing problem is Apophis, a 300-m asteroid that may be on a collision course with the Earth and is due to come by on April 13, 2029. It is unlikely to hit the Earth on that pass, but it will return again in 2036. If Apophis passes through a 600-m keyhole on its 2029 pass, it is expected to hit the Earth in 2036. causing great damage. There are plans to deflect Apophis when it comes by in 2029. For example, we could hit it with a 10- to 150-kg impactor accelerated by a solar sail. The impactor is launched from the Earth to start orbiting the Sun in the same direction as the Earth and Apophis. The idea is to use a solar sail to accelerate the impactor so that it reverses direction and collides head-on with Apophis at 8090 km/s and thereby keeps Apophis out of the keyhole. Consider the momentum in the impactors orbit (Fig. P34.75) when the solar sail makes an angle of = 60 with the tangent to its orbit. Current solar sails may be about 40 m on a side, but the hope is to construct some that are about 160 m on a side. Estimate the impactors tangential acceleration when it is about 1 AU from the Sun. Keep in mind that the sail is neither a perfect absorber nor a perfect reflector, and a heavier impactor would presumably be equipped with a larger sail. Dont be surprised by what may seem like a very small acceleration. FIGURE P34.75A microscopic spherical dust particle of radius 2m and mass 10g 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?A 2.50-m-diameter university communications satellite dish receives TV signals that have a maximum electric field strength (for one channel) of 7.50 (V/m. (See Figure 24.28.) (a) What is the intensity of this wave? (b) What is the power received by the antenna? (c) If the orbiting satellite broadcasts uniformly over an area of 1.501013m2 (a large fraction of North America), how much power does it radiate? Figure 24.28 Satellite dishes receive TV signals sent from orbit. Although the signals are quite weak, the receiver can detect them by being tuned to resonate at their frequency.
- Professor Edward Ney was the founder of infrared astronomy at the University of Minnesota. In his later years, he wore an artificial pacemaker. Always an experimentalist, Ney often held a strong laboratory magnet near his chest to see what effect it had on his pacemaker. Perhaps he was using the magnet to throw switches that control different modes of operation. An admiring student (without an artificial pacemaker) thought it would be fun to imitate this great man by holding a strong magnet to his own chest. The natural pacemaker of the heart (known as the sinoatrial node) carries a current of about 0.5 mA. Estimate the magnetic force exerted on a natural pacemaker by a strong magnet held to the chest. How do you think the student might have felt during the experiment? Explain your geometric assumptions. Hints: See Table 30.1 (page 941) to estimate the magnetic field, and assume the field is roughly uniform. Use Figure P30.58 to estimate the size of the sinoatrial node; your heart is about the size of your fist. FIGURE P30.58If you wish to detect details of the size of atoms (about 0.2 nm) with electromagnetic radiation, it must have a wavelength of about this size. (a) What is its frequency? (b) What type of electromagnetic radiation might this be?An electromagnetic radiation source radiates uniformly in all directions. How does the magnitude of the electric field strength Em vary with distance r from the source? (Think about what conservation of energy implies about how the Intensity varies with distance r from the source) a.Em is proportional to 1/r b.Em is constant for electromagnetic waves c.Em is proportional to 1/r3 d.Em is proportional to 1/r2
- A candle radiates light equally in all directions at an average rate of 80 W. At a certain distance from the candle, a derector measures a maximun electric field magnitude of 27.7 N/C. A) Calculate the average intensity of the candlelight at the ditector. B) Calculate the distance between the detector and the candle.A LASIK vision correction system uses a laser that emits 10-ns-long pulses of light, each with 2.5 mJ of energy. The laser is focused to a 0.85-mm-diameter circle. a. What is the average power of each laser pulse in units of watts? b. Determine the intensity of the laser light at the focus point. c. What is the electric field amplitude of the laser light at the focus point?Around the core of a nuclear reactor shielded by a large pool of water, Cerenkov radiation appears as a blue glow (see figure below). Cerenkov radiation occurs when a particle travels faster through a medium than the speed of light in that medium. It is the electromagnetic equivalent of a bow wave or a sonic boom. An electron is traveling through water at a speed 7.2% faster than the speed of light in water. U.S. Department of Energy/Photo Researchers, Inc. (a) Determine the electron's total energy. X Your response differs from the correct answer by more than 10%. Double check your calculations. MeV (b) Determine the electron's kinetic energy. X Your response differs from the correct answer by more than 100%. MeV (c) Determine the electron's momentum. X Your response differs from the correct answer by more than 10%. Double check your calculations. MeV/c (d) Find the angle between the shock wave and the electron's direction of motion. O
- Around the core of a nuclear reactor shielded by a large pool of water, Cerenkov radiation appears as a blue glow (see figure below). Cerenkov radiation occurs when a particle travels faster through a medium than the speed of light in that medium. It is the electromagnetic equivalent of a bow wave or a sonic boom. An electron is traveling through water at a speed 7.2% faster than the speed of light in water. U.S. Department of Energy/Photo Researchers, Inc. (a) Determine the electron's total energy. MeV (b) Determine the electron's kinetic energy. MeV (c) Determine the electron's momentum. MeV/c (d) Find the angle between the shock wave and the electron's direction of motion. OCalculate the electric field amplitude and the energy density of a plane wave of intensity I=1000Wm^-21. List the following types of electromagnetic radiation in order of increasing wavelength: visible light (v), infrared light (i), ultraviolet light (u), gamma rays (g), tv signals (t), x-rays (x), and microwaves (m). A. g,t,x,v,i,u B. t,x,g,i,u,v C. v,u,i,g,x,t D. g,x,u,v,i,t