Download Chapter 24: Electromagnetic Waves

Chapter 24: Electromagnetic Waves
1. In an RC circuit, the capacitor begins to discharge. (i) During the discharge, in the
region of space between the plates of the capacitor, is there (a) conduction current but no
displacement current, (b) displacement current but no conduction current, (c) both
conduction and displacement current, or (d) no current of any type? (ii) During the
discharge, in the region of space between the plates of the capacitor, is there (a) an
electric field but no magnetic field, (b) a magnetic field but no electric field, (c) both
electric and magnetic fields, or (d) no fields of any type?
Answer: (i), (b). There can be no conduction current because there is no conductor
between the plates. There is a time-varying electric field because of the decreasing charge
on the plates, and the time-varying electric flux represents a displacement current. (ii),
(c). There is a time-varying electric field because of the decreasing charge on the plates.
This time-varying electric field produces a magnetic field.
2. An electromagnetic wave propagates in the −y direction. The electric field at a point in
space is momentarily oriented in the +x direction. Is the magnetic field at that point
momentarily oriented in the (a) −x direction, (b) +y direction, (c) +z direction, or (d) −z
direction?
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Answer: (c). The B field must be in the +z direction so that the Poynting vector is
directed along the −y direction.
3. Which of the following quantities does not vary in time for plane electromagnetic
waves? (a) magnitude of the Poynting vector (b) energy density uE (c) energy density uB
(d) wave intensity
Answer: (d). The first three choices are instantaneous values and vary in time. The wave
intensity is an average over a full cycle.
4. In an apparatus such as that in Figure 24.11, suppose the black disk is replaced by one
with half the radius. Which of the following are different after the disk is replaced? (a)
radiation pressure on the disk (b) radiation force on the disk (c) radiation momentum
delivered to the disk in a given time interval
Figure 24.11 An apparatus for measuring the pressure exerted by light. In practice, the system is contained
in a high vacuum.
Answer: (b), (c). The radiation pressure (a) does not change because pressure is force per
unit area. In (b), the smaller disk absorbs less radiation, resulting in a smaller force. For
the same reason, the momentum in (c) is reduced.
5. In many kitchens, a microwave oven is used to cook food. The frequency of the
microwaves is on the order of 1010 Hz. The wavelengths of these microwaves are on the
order of (a) kilometers, (b) meters, (c) centimeters, or (d) micrometers.
Answer: (c). The order of magnitude of the wavelengths can be found either from the
equation c = λf or from Figure 24.12.
Figure 24.12 The electromagnetic spectrum. Note the overlap between adjacent wave types. The expanded
view to the right shows details of the visible spectrum.
6. A radio wave of frequency on the order of 105 Hz is used to carry a sound wave with a
frequency on the order of 103 Hz. The wavelength of this radio wave is on the order of
(a) kilometers, (b) meters, (c) centimeters, or (d) micrometers.
Answer: (a). The order of magnitude of the wavelengths can be found either from the
equation c = λf or from Figure 24.12.
7. A polarizer for microwaves can be made as a grid of parallel metal wires about a
centimeter apart. Is the electric field vector for microwaves transmitted through this
polarizer (a) parallel or (b) perpendicular to the metal wires?
Answer: (b). Electric field vectors parallel to the metal wires cause electrons in the metal
to oscillate along the wires. Therefore, the energy from the waves with these electric field
vectors is transferred to the metal by accelerating these electrons and is eventually
transformed to internal energy through the resistance of the metal. Waves with electric
field vectors perpendicular to the metal wires are not able to accelerate electrons and pass
through.