Additional Problems

| 41 | Some of the X-rays produced in an X-ray machine have a wavelength of 2.1 nm. What is the frequency of these electromagnetic waves?

| 42 | The maximum strength of the magnetic field in an electromagnetic wave is . What is the maximum strength of the wave’s electric field?

| 43 | ssm www An AM station is broadcasting a radio wave whose frequency is 1400 kHz. The value of the capacitance in Figure 24-5 is . What must be the value of the inductance in order that this station can be tuned in by the radio?

| 44 | TV channel 3 (VHF) broadcasts at a frequency of 63.0 MHz. TV channel 23 (UHF) broadcasts at a frequency of 527 MHz. Find the ratio (VHF/UHF) of the wavelengths for these channels.

| 45 | ssm A future space station in orbit about the earth is being powered by an electromagnetic beam from the earth. The beam has a cross-sectional area of 135 m2 and transmits an average power of . What are the rms values of the (a) electric and (b) magnetic fields?

| 46 | Multiple-Concept Example 6 explores the concepts that are involved in this problem. Suppose that the police car in that example is moving to the right at 27 m/s, while the speeder is coming up from behind at a speed of 39 m/s, both speeds being with respect to the ground. Assume that the electromagnetic wave emitted by the radar gun has a frequency of . Find the difference between the frequency of the wave that returns to the police car after reflecting from the speeder’s car and the original frequency emitted by the police car.

| 47 | ssm In the polarizer/analyzer combination in Figure 24-21, 90.0% of the light intensity falling on the analyzer is absorbed. Determine the angle between the transmission axes of the polarizer and the analyzer.

* | 48 | The electromagnetic wave that delivers a cellular phone call to a car has a magnetic field with an rms value of . The wave passes perpendicularly through an open window, the area of which is 0.20 m2. How much energy does this wave carry through the window during a 45-s phone call?

* | 49 | In a traveling electromagnetic wave, the electric field is represented mathematically as

where E0 is the maximum field strength. (a) What is the frequency of the wave? (b) This wave and the wave that results from its reflection can form a standing wave, in a way similar to that in which standing waves can arise on a string (see Section 17.5). What is the separation between adjacent nodes in the standing wave?

* | 50 | A beam of polarized light has an average intensity of 15 W/m2 and is sent through a polarizer. The transmission axis makes an angle of 25° with respect to the direction of polarization. Determine the rms value of the electric field of the transmitted beam.

* | 51 | ssm www The power radiated by the sun is . The earth orbits the sun in a nearly circular orbit of radius . The earth’s axis of rotation is tilted by 27° relative to the plane of the orbit (see the drawing), so sunlight does not strike the equator perpendicularly. What power strikes a 0.75-m2 patch of flat land at the equator at point Q?

* | 52 | A heat lamp emits infrared radiation whose rms electric field is . (a) What is the average intensity of the radiation? (b) The radiation is focused on a person’s leg over a circular area of radius 4.0 cm. What is the average power delivered to the leg? (c) The portion of the leg being radiated has a mass of 0.28 kg and a specific heat capacity of 3500 J/(kg · C°). How long does it take to raise its temperature by 2.0 C°? Assume that there is no other heat transfer into or out of the portion of the leg being heated.

* | 53 | Interactive Solution 24.53 at provides one model for problems like this one. The drawing shows an edge-on view of the solar panels on a communications satellite. The dashed line specifies the normal to the panels. Sunlight strikes the panels at an angle with respect to the normal. If the solar power impinging on the panels is 2600 W when , what is it when ?

** | 54 | Suppose that the light falling on the polarizer in Figure 24-21 is partially polarized (average intensity ) and partially unpolarized (average intensity . The total incident intensity is , and the percentage polarization is . When the polarizer is rotated in such a situation, the intensity reaching the photocell varies between a minimum value of and a maximum value of . Show that the percentage polarization can be expressed as .

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