Solutions to Electromagnetism Exercises: Wave Polarization, Microwaves, and AC Motors | Assignments Classical Physics

HW9 Solutions

E13.10 Since accelerating electric charge is what produces radio waves, the sudden

accelerations experienced by currents as they flow around sharp bends lead to intense and

wasteful electromagnetic radiation.

E13.13 The emitted EM wave has a vertical polarization, i.e. the electric field of the EM wave is

oscillating in the vertical plane with the E field parallel to the motion of the charge.

E13.14 The emitted EM wave is vertically polarized because the electric field of the wave is

oscillating in the vertical direction (just as in exercise 13). Why? Because the magnetic

field from the compass is oscillating in the horizontal direction and an EM wave has its

electric field and magnetic field perpendicular to each other (and both are perpendicular

to the direction of propagation of the wave).

E13.16 For AM, the loudness depends on the amplitude of the modulation of the carrier wave.

Thus loud parts of the signal may remain detectable even when quieter parts are too weak

to pick up. For FM, the loudness is encoded in the frequency variation of the carrier wave

and the carrier wave has constant amplitude. Thus it’s “all or nothing” as far as

receiving FM is concerned.

E13.20 Aluminum trays would reflect the microwaves making it difficult to heat the food

properly.

E13.22 In a microwave oven, the potato’s water absorbs microwaves. The microwave energy

becomes thermal energy and the potato’s temperature rises relatively uniformly. In an

ordinary oven, heat flows gradually into the potato through its surface and its temperature

rises nonuniformly. The middle of the potato cooks last. In an ordinary oven it is infrared

radiation which is absorbed on the surface, unlike microwaves which can penetrate the

potato. This is due to the higher frequency of infrared waves compared to microwaves.

C13.4 a) wavelength = speed/frequency.

So, telephone wavelength = (3 x 108 m/s)/(825 x 106 Hz) = 0.36 m =36 cm.

In same way, the base wavelength = 0.34 m = 34 cm.

b) ¼ of a wavelength, i.e. 36/4 cm = 9 cm.

c) There are only 832 channels available in each cell, not enough for each of the 900

people to have a channel.

d) People located along the line of the antenna would receive no signal since the EM

wave amplitude is zero in this direction (recall the demonstration that I did in class with

the radio transmitter and receiving antenna).

e) This is basically the same question as (d). The electric field of the incoming wave from

the base station antenna accelerates electrons in the vertical direction. This will drive a

current in the receiving antenna only if it is oriented at least partially in the vertical

direction.

f) The EM waves can be absorbed by the ground or reflected by the metal building.

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HW9 Solutions

E13.10 Since accelerating electric charge is what produces radio waves, the sudden accelerations experienced by currents as they flow around sharp bends lead to intense and wasteful electromagnetic radiation.

E13.13 The emitted EM wave has a vertical polarization, i.e. the electric field of the EM wave is oscillating in the vertical plane with the E field parallel to the motion of the charge.

E13.14 The emitted EM wave is vertically polarized because the electric field of the wave is oscillating in the vertical direction (just as in exercise 13). Why? Because the magnetic field from the compass is oscillating in the horizontal direction and an EM wave has its electric field and magnetic field perpendicular to each other (and both are perpendicular to the direction of propagation of the wave).

E13.16 For AM, the loudness depends on the amplitude of the modulation of the carrier wave. Thus loud parts of the signal may remain detectable even when quieter parts are too weak to pick up. For FM, the loudness is encoded in the frequency variation of the carrier wave and the carrier wave has constant amplitude. Thus it’s “all or nothing” as far as receiving FM is concerned.

E13.20 Aluminum trays would reflect the microwaves making it difficult to heat the food properly.

E13.22 In a microwave oven, the potato’s water absorbs microwaves. The microwave energy becomes thermal energy and the potato’s temperature rises relatively uniformly. In an ordinary oven, heat flows gradually into the potato through its surface and its temperature rises nonuniformly. The middle of the potato cooks last. In an ordinary oven it is infrared radiation which is absorbed on the surface, unlike microwaves which can penetrate the potato. This is due to the higher frequency of infrared waves compared to microwaves.

C13.4 a) wavelength = speed/frequency.

So, telephone wavelength = (3 x 10^8 m/s)/(825 x 10^6 Hz) = 0.36 m =36 cm. In same way, the base wavelength = 0.34 m = 34 cm. b) ¼ of a wavelength, i.e. 36/4 cm = 9 cm. c) There are only 832 channels available in each cell, not enough for each of the 900 people to have a channel. d) People located along the line of the antenna would receive no signal since the EM wave amplitude is zero in this direction (recall the demonstration that I did in class with the radio transmitter and receiving antenna). e) This is basically the same question as (d). The electric field of the incoming wave from the base station antenna accelerates electrons in the vertical direction. This will drive a current in the receiving antenna only if it is oriented at least partially in the vertical direction. f) The EM waves can be absorbed by the ground or reflected by the metal building.

g) The bandwidth of each channel is 30 kHz. If your phone generates waves more than 15 kHz from the center of its band, then those waves will fall into a neighboring band and interfere with someone else’s communications. h) If the waves are too intense, then someone in the next cell will pick them up and there will be interference (i.e., crosstalk) between the two cells.

C11.12 a) The alternating current in the coil produces an alternating magnetic field with which the permanent magnet interacts.

b) If the AC power is delivered at 60Hz, there are 60 complete cycles per second.

c) Direct current from the battery would generate a constant magnetic field in the coil, which would produce any back and forth motion of the permanent magnet.

d) Universal motors (as explained in the text) are designed to turn only in one direction regardless of the direction of the applied voltage.

e) If you reverse the current into the coil of a DC motor, you reverse the forces between the coil and the permanent magnet. So, if you reverse the current direction the motor will spin in the reversed direction.

Solutions to Electromagnetism Exercises: Wave Polarization, Microwaves, and AC Motors, Assignments of Classical Physics

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