Future space rockets might propel themselves by firing

How do fields transform?

What is Maxwells theory of electromagnetism?

What are electromagnetic waves?

What is polarization?

A laboratory experimenter has created the parallel electric and magnetic fields E u = 10,000 ni V/m and B u = 0.10 ni T. A proton is shot into these fields with velocity v u = 1.0 * 105 nj m/s. What is the electric field in the protons reference frame?

The first diagram shows electric and magnetic fields in reference frame A. Which diagram shows the fields in frame B?

The 1.0 T field of a large laboratory magnet points straight up. A rocket flies past the laboratory, parallel to the ground, at 1000 m/s. What are the fields between the magnets pole tips as measured very quickly!by scientists on the rocket?

The electric field in four identical capacitors is shown as a function of time. Rank in order, from largest to smallest, the magnetic field strength at the outer edge of the capacitor at time T.

A 2.0-cm-diameter parallel-plate capacitor with a 1.0 mm spacing is being charged at the rate 0.50 C/s. What is the magnetic field strength inside the capacitor at a point 0.50 cm from the axis?

An electromagnetic wave is propagating in the positive x-direction. At this instant of time, what is the direction of E u at the center of the rectangle? v u z y u B(x) u B(x + x) x x a. In the positive x-direction b. In the negative x-direction c. In the positive y-direction d. In the negative y-direction e. In the positive z-direction f. In the negative z-direction

A digital cell phone broadcasts a 0.60 W signal at a frequency of 1.9 GHz. What are the amplitudes of the electric and magnetic fields at a distance of 10 cm, about the distance to the center of the users brain?

An electromagnetic wave is traveling in the positive y-direction. The electric field at one instant of time is shown at one position. The magnetic field at this position points a. In the positive x-direction. b. In the negative x-direction. c. In the positive y-direction. d. In the negative y-direction. e. Toward the origin. f. Away from the origin.

A low-cost way of sending spacecraft to other planets would be to use the radiation pressure on a solar sail. The intensity of the suns electromagnetic radiation at distances near the earths orbit is about 1300 W/m2 . What size sail would be needed to accelerate a 10,000 kg spacecraft toward Mars at 0.010 m/s2 ?

The amplitude of the oscillating electric field at your cell phone is 4.0 mV/m when you are 10 km east of the broadcast antenna. What is the electric field amplitude when you are 20 km east of the antenna? a. 1.0 mV/m b. 2.0 mV/m c. 4.0 mV/m d. Theres not enough information to tell.

Unpolarized light of equal intensity is incident on four pairs of polarizing filters. Rank in order, from largest to smallest, the intensities Ia to Id transmitted through the second polarizer of each pair. 30 (a) 30 60 (b) 30 30 (c) 60 30 (d)

Future space rockets might propel themselves by firing laser beams, rather than exhaust gases, out the back. The acceleration would be small, but it could continue for months or years in the vacuum of space. Consider a 1200 kg unmanned space probe powered by a 15 MW laser. After one year, how far will it have traveled and how fast will it be going?

Andre is flying his spaceship to the left through the laboratory magnetic field of FIGURE Q31.1. a. Does Andre see a magnetic field? If so, in which direction does it point? b. Does Andre see an electric field? If so, in which direction does it point?

Sharon drives her rocket through the magnetic field of FIGURE Q31.2 traveling to the right at a speed of 1000 m/s as measured by Bill. As she passes Bill, she shoots a positive charge backward at a speed of 1000 m/s relative to her. a. According to Bill, what kind of force or forces act on the charge? In which directions? Explain. b. According to Sharon, what kind of force or forces act on the charge? In which directions? Explain.

If you curl the fingers of your right hand as shown, are the electric fluxes in FIGURE Q31.3 positive or negative?

What is the current through surface S in FIGURE Q31.4 if you curl your right fingers in the direction of the arrow?

Is the electric field strength in FIGURE Q31.5 increasing, decreasing, or not changing? Explain.

Do the situations in FIGURE Q31.6 represent possible electromagnetic waves? If not, why not?

In what directions are the electromagnetic waves traveling in FIGURE Q31.7 ?

The intensity of an electromagnetic wave is 10 W/m2 . What will the intensity be if: a. The amplitude of the electric field is doubled? b. The amplitude of the magnetic field is doubled? c. The amplitudes of both the electric and the magnetic fields are doubled? d. The frequency is doubled?

Older televisions used a loop antenna like the one in FIGURE Q31.9. How does this antenna work?

A vertically polarized electromagnetic wave passes through the five polarizers in FIGURE Q31.10. Rank in order, from largest to smallest, the transmitted intensities Ia to Ie.

FIGURE EX31.1 shows the electric and magnetic field in frame A. A rocket in frame B travels parallel to one of the axes of the A coordinate system. Along which axis must the rocket travel, and in which direction, in order for the rocket scientists to measure (a) BB 7 BA, (b) BB = BA, and (c) BB 6 BA?

A rocket cruises past a laboratory at 1.00 * 106 m/s in the positive x-direction just as a proton is launched with velocity (in the laboratory frame) v u = 11.41 * 106 ni + 1.41 * 106 nj2 m/s. What are the protons speed and its angle from the y-axis in (a) the laboratory frame and (b) the rocket frame?

Laboratory scientists have created the electric and magnetic fields shown in FIGURE EX31.3. These fields are also seen by scientists who zoom past in a rocket traveling in the x-direction at 1.0 * 106 m/s. According to the rocket scientists, what angle does the electric field make with the axis of the rocket?

Scientists in the laboratory create a uniform electric field E u =1.0 * 106 k n V/m in a region of space where B u = 0 u . What are the fields in the reference frame of a rocket traveling in the positive x-direction at 1.0 * 106 m/s?

A rocket zooms past the earth at v = 2.0 * 106 m/s. Scientists on the rocket have created the electric and magnetic fields shown in FIGURE EX31.5. What are the fields measured by an earthbound scientist?

The magnetic field is uniform over each face of the box shown in FIGURE EX31.6. What are the magnetic field strength and direction on the front surface?

Show that the quantity P01de/dt2 has units of current.

Show that the displacement current inside a parallel-plate capacitor can be written C1dVC/dt2.

What capacitance, in mF, has its potential difference increasing at 1.0 * 106 V/s when the displacement current in the capacitor is 1.0 A?

A 5.0-cm-diameter parallel-plate capacitor has a 0.50 mm gap. What is the displacement current in the capacitor if the potential difference across the capacitor is increasing at 500,000 V/s?

A 10-cm-diameter parallel-plate capacitor has a 1.0 mm spacing. The electric field between the plates is increasing at the rate 1.0 * 106 V/ms. What is the magnetic field strength (a) on the axis, (b) 3.0 cm from the axis, and (c) 7.0 cm from the axis?

What is the magnetic field amplitude of an electromagnetic wave whose electric field amplitude is 10 V/m?

What is the electric field amplitude of an electromagnetic wave whose magnetic field amplitude is 2.0 mT?

The magnetic field of an electromagnetic wave in a vacuum is Bz = 13.00 mT2 sin311.00 * 107 2x - vt4, where x is in m and t is in s. What are the waves (a) wavelength, (b) frequency, and (c) electric field amplitude?

The electric field of an electromagnetic wave in a vacuum is Ey = 120.0 V/m2 cos316.28 * 108 2x - vt4, where x is in m and t is in s. What are the waves (a) wavelength, (b) frequency, and (c) magnetic field amplitude?

a. What is the magnetic field amplitude of an electromagnetic wave whose electric field amplitude is 100 V/m? b. What is the intensity of the wave?

A radio wave is traveling in the negative y-direction. What is the direction of E u at a point where B u is in the positive x-direction?

A radio receiver can detect signals with electric field amplitudes as small as 300 mV/m. What is the intensity of the smallest detectable signal?

A helium-neon laser emits a 1.0-mm-diameter laser beam with a power of 1.0 mW. What are the amplitudes of the electric and magnetic fields of the light wave?

A radio antenna broadcasts a 1.0 MHz radio wave with 25 kW of power. Assume that the radiation is emitted uniformly in all directions. a. What is the waves intensity 30 km from the antenna? b. What is the electric field amplitude at this distance?

A 200 MW laser pulse is focused with a lens to a diameter of 2.0 mm. a. What is the laser beams electric field amplitude at the focal point? b. What is the ratio of the laser beams electric field to the electric field that keeps the electron bound to the proton of a hydrogen atom? The radius of the electron orbit is 0.053 nm

A 1000 W carbon-dioxide laser emits light with a wavelength of 10 mm into a 3.0-mm-diameter laser beam. What force does the laser beam exert on a completely absorbing target?

At what distance from a 10 W point source of electromagnetic waves is the magnetic field amplitude 1.0 mT?

Only 25% of the intensity of a polarized light wave passes through a polarizing filter. What is the angle between the electric field and the axis of the filter?

FIGURE EX31.25 shows a vertically polarized radio wave of frequency 1.0 * 106 Hz traveling into the page. The maximum electric field strength is 1000 V/m. What are a. The maximum magnetic field strength? b. The magnetic field strength and direction at a point where E u = 1500 V/m, down2?

Unpolarized light with intensity 350 W/m2 passes first through a polarizing filter with its axis vertical, then through a second polarizing filter. It emerges from the second filter with intensity 131 W/m2 . What is the angle from vertical of the axis of the second polarizing filter?

A 200 mW vertically polarized laser beam passes through a polarizing filter whose axis is 35 from horizontal. What is the power of the laser beam as it emerges from the filter?

What are the electric field strength and direction at the position of the electron in FIGURE P31.28 ?

What is the force (magnitude and direction) on the proton in FIGURE P31.29? Give the direction as an angle cw or ccw from vertical

What electric field strength and direction will allow the proton in FIGURE P31.30 to pass through this region of space without being deflected?

A proton is fired with a speed of 1.0 * 106 m/s through the parallel-plate capacitor shown in FIGURE P31.31. The capacitors electric field is E u = 11.0 * 105 V/m, down2. a. What magnetic field B u , both strength and direction, must be applied to allow the proton to pass through the capacitor with no change in speed or direction? b. Find the electric and magnetic fields in the protons reference frame.c. How does an experimenter in the protons frame explain that the proton experiences no force as the charged plates fly by?

An electron travels with v u = 5.0 * 106 ni m/s through a point in space where E u = 12.0 * 105 ni - 2.0 * 105 nj2 V/m and B u = -0.10 k n T. What is the force on the electron?

In FIGURE P31.33, a circular loop of radius r travels with speed v along a charged wire having linear charge density l. The wire is at rest in the laboratory frame, and it passes through the center of the loop. a. What are E u and B u at a point on the loop as measured by a scientist in the laboratory? Include both strength and direction. b. What are the fields E u and B u at a point on the loop as measured by a scientist in the frame of the loop? c. Show that an experimenter in the loops frame sees a current I = lv passing through the center of the loop. d. What electric and magnetic fields would an experimenter in the loops frame calculate at distance r from the current of part c? e. Show that your fields of parts b and d are the same.

The magnetic field inside a 4.0-cm-diameter superconducting solenoid varies sinusoidally between 8.0 T and 12.0 T at a frequency of 10 Hz. a. What is the maximum electric field strength at a point 1.5 cm from the solenoid axis? b. What is the value of B at the instant E reaches its maximum value?

A simple series circuit consists of a 150 resistor, a 25 V battery, a switch, and a 2.5 pF parallel-plate capacitor (initially uncharged) with plates 5.0 mm apart. The switch is closed at t = 0 s. a. After the switch is closed, find the maximum electric flux and the maximum displacement current through the capacitor. b. Find the electric flux and the displacement current at t = 0.50 ns

A wire with conductivity s carries current I. The current is increasing at the rate dI/dt. a. Show that there is a displacement current in the wire equal to 1P0/s21dI/dt2. b. Evaluate the displacement current for a copper wire in which the current is increasing at 1.0 * 106 A/s

A 10 A current is charging a 1.0-cm-diameter parallel-plate capacitor. a. What is the magnetic field strength at a point 2.0 mm radially from the center of the wire leading to the capacitor? b. What is the magnetic field strength at a point 2.0 mm radially from the center of the capacitor?

FIGURE P31.38 shows the voltage across a 0.10 mF capacitor. Draw a graph showing the displacement current through the capacitor as a function of time.

FIGURE P31.39 shows the electric field inside a cylinder of radius R = 3.0 mm. The field strength is increasing with time as E = 1.0 * 108 t 2 V/m, where t is in s. The electric field outside the cylinder is always zero, and the field inside the cylinder was zero for t 6 0. a. Find an expression for the electric flux e through the entire cylinder as a function of time. b. Draw a picture showing the magnetic field lines inside and outside the cylinder. Be sure to include arrowheads showing the fields direction. c. Find an expression for the magnetic field strength as a function of time at a distance r 6 R from the center. Evaluate the magnetic field strength at r = 2.0 mm, t = 2.0 s. d. Find an expression for the magnetic field strength as a function of time at a distance r 7 R from the center. Evaluate the magnetic field strength at r = 4.0 mm, t = 2.0 s.

A long, thin superconducting wire carrying a 15 A current passes through the center of a thin, 2.0-cm-diameter ring. A uniform electric field of increasing strength also passes through the ring, parallel to the wire. The magnetic field through the ring is zero. a. At what rate is the electric field strength increasing? b. Is the electric field in the direction of the current or opposite to the current?

A 1.0 mF capacitor is discharged, starting at t = 0 s. The displacement current through the plates is Idisp = 110 A2exp1-t/2.0 ms2. What was the capacitors initial voltage 1VC20

At one instant, the electric and magnetic fields at one point of an electromagnetic wave are E u = 1200 ni + 300 nj - 50 k n2 V/m and B u = B017.3 ni - 7.3 nj + a k n2 mT. a. What are the values of a and B0? b. What is the Poynting vector at this time and position?

a. Show that uE and uB, the energy densities of the electric and magnetic fields, are equal to each other in an electromagnetic wave. In other words, show that the waves energy is divided equally between the electric field and the magnetic field. b. What is the total energy density in an electromagnetic wave of intensity 1000 W/m2 ?

The intensity of sunlight reaching the earth is 1360 W/m2 . a. What is the power output of the sun? b. What is the intensity of sunlight reaching Mar

Assume that a 7.0-cm-diameter, 100 W lightbulb radiates all its energy as a single wavelength of visible light. Estimate the electric and magnetic field strengths at the surface of the bulb.

The electric field of a 450 MHz radio wave has a maximum rate of change of 4.5 * 1011 1V/m2/s. What is the waves magnetic field amplitude?

When the Voyager 2 spacecraft passed Neptune in 1989, it was 4.5 * 109 km from the earth. Its radio transmitter, with which it sent back data and images, broadcast with a mere 21 W of power. Assuming that the transmitter broadcast equally in all directions, a. What signal intensity was received on the earth? b. What electric field amplitude was detected? The received signal was somewhat stronger than your result because the spacecraft used a directional antenna, but not by much.

In reading the instruction manual that came with your garagedoor opener, you see that the transmitter unit in your car produces a 250 mW, 350 MHz signal and that the receiver unit is supposed to respond to a radio wave at this frequency if the electric field amplitude exceeds 0.10 V/m. You wonder if this is really true. To find out, you put fresh batteries in the transmitter and start walking away from your garage while opening and closing the door. Your garage door finally fails to respond when youre 42 m away. What is the electric field amplitude at the receiver when it first fails?

The maximum electric field strength in air is 3.0 MV/m. Stronger electric fields ionize the air and create a spark. What is the maximum power that can be delivered by a 1.0-cm-diameter laser beam propagating through air?

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 beam is focused to a 0.85-mm-diameter circle on the cornea. What is the electric field amplitude of the light wave at the cornea?

The intensity of sunlight reaching the earth is 1360 W/m2 . Assuming all the sunlight is absorbed, what is the radiationpressure force on the earth? Give your answer (a) in newtons and (b) as a fraction of the suns gravitational force on the earth

For radio and microwaves, the depth of penetration into the human body is proportional to l1/2 . If 27 MHz radio waves penetrate to a depth of 14 cm, how far do 2.4 GHz microwaves penetrate?

A laser beam shines straight up onto a flat, black foil of mass m. a. Find an expression for the laser power P needed to levitate the foil. b. Evaluate P for a foil with a mass of 25 mg.

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?

Youve recently read about a chemical laser that generates a 20-cm-diameter, 25 MW laser beam. One day, after physics class, you start to wonder if you could use the radiation pressure from this laser beam to launch small payloads into orbit. To see if this might be feasible, you do a quick calculation of the acceleration of a 20-cm-diameter, 100 kg, perfectly absorbing block. What speed would such a block have if pushed horizontally 100 m along a frictionless track by such a laser?

Unpolarized light of intensity I0 is incident on three polarizing filters. The axis of the first is vertical, that of the second is 45 from vertical, and that of the third is horizontal. What light intensity emerges from the third filter?

Unpolarized light of intensity I0 is incident on two polarizing filters. The transmitted light intensity is I0 /10. What is the angle between the axes of the two filters?

Unpolarized light of intensity I0 is incident on a stack of 7 polarizing filters, each with its axis rotated 15 cw with respect to the previous filter. What light intensity emerges from the last filter?

A cube of water 10 cm on a side is placed in a microwave beam having E0 = 11 kV/m. The microwaves illuminate one face of the cube, and the water absorbs 80% of the incident energy. How long will it take to raise the water temperature by 50C? Assume that the water has no heat loss during this time.

An 80 kg astronaut has gone outside his space capsule to do some repair work. Unfortunately, he forgot to lock his safety tether in place, and he has drifted 5.0 m away from the capsule. Fortunately, he has a 1000 W portable laser with fresh batteries that will operate it for 1.0 h. His only chance is to accelerate himself toward the space capsule by firing the laser in the opposite direction. He has a 10-h supply of oxygen. How long will it take him to reach safety?

An electron travels with v u = 5.0 * 106 ni m/s through a point in space where B u = 0.10 nj T. The force on the electron at this point is F u = 19.6 * 10-14 ni - 9.6 * 10-14 k n2 N. What is the electric field?

The radar system at an airport broadcasts 11 GHz microwaves with 150 kW of power. An approaching airplane with a 31 m2 cross section is 30 km away. Assume that the radar broadcasts uniformly in all directions and that the airplane scatters microwaves uniformly in all directions. What is the electric field strength of the microwave signal received back at the airport 200 ms later?

Large quantities of dust should have been left behind after the creation of the solar system. Larger dust particles, comparable in size to soot and sand grains, are common. They create shooting stars when they collide with the earths atmosphere. But very small dust particles are conspicuously absent. Astronomers believe that the very small dust particles have been blown out of the solar system by the sun. By comparing the forces on dust particles, determine the diameter of the smallest dust particles that can remain in the solar system over long periods of time. Assume that the dust particles are spherical, black, and have a density of 2000 kg/m3 . The sun emits electromagnetic radiation with power 3.9 * 1026 W.

Consider current I passing through a resistor of radius r, length L, and resistance R. a. Determine the electric and magnetic fields at the surface of the resistor. Assume that the electric field is uniform throughout, including at the surface. b. Determine the strength and direction of the Poynting vector at the surface of the resistor. c. Show that the flux of the Poynting vector (i.e., the integral of S u # dA u ) over the surface of the resistor is I 2 R. Then give an interpretation of this result