Example 22-1 A Radio Wave
A certain FM radio station broadcasts at a frequency of 98.7 MHz (1 MHz = 106 Hz). In the wave that reaches the radio
in your car, the electric field amplitude is 6.00 * 10-2 V>m. Calculate the wavelength of the wave and the amplitude of
the magnetic field.
Set Up
We are given the wave frequency f and
the ­electric field amplitude E0. We use
Equation 22-2 to find the wavelength l
and Equation 22-4 to find the magnetic field
amplitude B0.
Propagation speed, frequency, and electric field, amplitude E0
wavelength of an electromagnetic
magnetic field,
wave:
c = fl
amplitude B0
(22-2)
Relation between the electric and
magnetic field amplitudes in an
electromagnetic wave:
B0 =
E0
c
(22-4)
direction of
wave propagation
wavelength
Solve
Use Equation 22-2 and the given frequency
f = 98.7 MHz = 98.7 * 106 Hz to solve for
the wavelength.
From Equation 22-2,
l =
3.00 * 108 m>s
c
m
=
= 3.04 #
6
f
s
Hz
98.7 * 10 Hz
Recall that 1 Hz = 1 s21, so the units of s and Hz cancel:
l = 3.04 m
Use Equation 22-4 and the value
E 0 = 6.00 * 10-2 V>m to solve for
the magnetic field amplitude.
From Equation 22-4,
B0 =
6.00 * 10-2 V>m
E0
V
s
= 2.00 * 10-10 a b a b
=
8
c
m
m
3.00 * 10 m>s
We learned in Section 17-3 that 1 V>m = 1 N>C, and in Section 19-3
we learned that 1 T = 1 1N # s2 > 1C # m2. So
B0 = 2.00 * 10-10 a
= 2.00 * 10-10 T
Reflect
s
N#s
N
b a b = 2.00 * 10-10 #
m
C
C m
Because the speed of light c has such a large value in m>s, the magnetic field amplitude B0 in tesla (T) is much smaller
than the electric field amplitude E0 in volts per meter (V>m). As we’ll see later in the chapter, however, the electric and
magnetic fields prove to be equally important in an electromagnetic wave in vacuum.
In this example we’ve seen how to relate the units of magnetic field (T) to those of electric field (V>m):
1 T = 1 1V>m2 # 1s>m2 = 1 V # s>m2. We’ll make use of this result in later examples.