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A certain electromagnetic wave has fields described by the following functions: E(x,t) = (60 V/m) cos(kx - ?t) j B(x,t) = B0 cos(kx - ?t) k where ? = 2?f and f = 100.7 MHz. a) Note that the electric field oscillates along the y-axis and the magnetic field oscillates along the z-axis. What direction does the wave travel? b) Determine the magnitude of the magnetic field B0. c) Determine the wavelength ?. The frequency of this wave identifies it as a radio wave. In fact, 100.7 MHz is just the station 100.7 WZLX on your FM radio. d) Suppose you wanted to produce a voltage across the two ends of an antenna by using the electric field of this wave to produce an electric force on the charges in the antenna. Which direction should you orient the antenna: along the x, y, or z axis? e) If the antenna is 0.8 m long, what is the amplitude of that voltage? f) Suppose instead that you wanted to move an antenna at a velocity v in order to cause a magnetic force to drive an emf across the antenna. You decide to hold the antenna in the same orientation as in part d. This means that we will get the same voltage as in part d, but we will also get additional emf from the magnetic force now. In what direction must the velocity vector v point to maximize this magnetic force: x, y, or z? g) The antenna is still 0.8 m long, and the speed is 25 m/s. What amplitude of emf is induced by this magnetic force? Now you see why it doesn't really matter which direction your car is going—that extra magnetic emf from (g) is very small compared to the voltage from (e). So the signal is driven almost exclusively by the electric field piece of the EM wave. h) If that's true, then why bother with the magnetic field at all? Couldn't we just produce a pure E wave without the B? This is a somewhat open-ended question so your explanation is more important than the actual answer.

A certain electromagnetic wave has fields described by the following functions:
E(x,t) = (60 V/m) cos(kx - ?t) j
B(x,t) = B0 cos(kx - ?t) k
where ? = 2?f and f = 100.7 MHz.

a) Note that the electric field oscillates along the y-axis and the magnetic field oscillates along the z-axis. What direction does the wave travel?

b) Determine the magnitude of the magnetic field B0.

c) Determine the wavelength ?.

The frequency of this wave identifies it as a radio wave. In fact, 100.7 MHz is just the station 100.7 WZLX on your FM radio.

d) Suppose you wanted to produce a voltage across the two ends of an antenna by using the electric field of this wave to produce an electric force on the charges in the antenna. Which direction should you orient the antenna: along the x, y, or z axis?

e) If the antenna is 0.8 m long, what is the amplitude of that voltage?

f) Suppose instead that you wanted to move an antenna at a velocity v in order to cause a magnetic force to drive an emf across the antenna. You decide to hold the antenna in the same orientation as in part d. This means that we will get the same voltage as in part d, but we will also get additional emf from the magnetic force now. In what direction must the velocity vector v point to maximize this magnetic force: x, y, or z?

g) The antenna is still 0.8 m long, and the speed is 25 m/s. What amplitude of emf is induced by this magnetic force?

Now you see why it doesn't really matter which direction your car is going—that extra magnetic emf from (g) is very small compared to the voltage from (e). So the signal is driven almost exclusively by the electric field piece of the EM wave.

h) If that's true, then why bother with the magnetic field at all? Couldn't we just produce a pure E wave without the B? This is a somewhat open-ended question so your explanation is more important than the actual answer.

A certain electromagnetic wave has fields described by the following functions:
E(x,t) = (60 V/m) cos(kx - ?t) j
B(x,t) = B0 cos(kx - ?t) k
where ? = 2?f and f = 100.7 MHz.

a) Note that the electric field oscillates along the y-axis and the magnetic field oscillates along the z-axis. What direction does the wave travel?

b) Determine the magnitude of the magnetic field B0.

c) Determine the wavelength ?.

The frequency of this wave identifies it as a radio wave. In fact, 100.7 MHz is just the station 100.7 WZLX on your FM radio.

d) Suppose you wanted to produce a voltage across the two ends of an antenna by using the electric field of this wave to produce an electric force on the charges in the antenna. Which direction should you orient the antenna: along the x, y, or z axis?

e) If the antenna is 0.8 m long, what is the amplitude of that voltage?

f) Suppose instead that you wanted to move an antenna at a velocity v in order to cause a magnetic force to drive an emf across the antenna. You decide to hold the antenna in the same orientation as in part d. This means that we will get the same voltage as in part d, but we will also get additional emf from the magnetic force now. In what direction must the velocity vector v point to maximize this magnetic force: x, y, or z?

g) The antenna is still 0.8 m long, and the speed is 25 m/s. What amplitude of emf is induced by this magnetic force?

Now you see why it doesn't really matter which direction your car is going—that extra magnetic emf from (g) is very small compared to the voltage from (e). So the signal is driven almost exclusively by the electric field piece of the EM wave.

h) If that's true, then why bother with the magnetic field at all? Couldn't we just produce a pure E wave without the B? This is a somewhat open-ended question so your explanation is more important than the actual answer.

Added by Dolores G.

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