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Magazine Problem 25
In the United States, the ac household current oscillates at a frequency of
\(60 \mathrm{Hz}\). In the time it takes for the current to make one
oscillation, how far has the electromagnetic wave traveled from the current
carrying wire? This distance is the wavelength of a \(60-\mathrm{Hz}\) EM wave.
Compare this length with the distance from Boston to Los Angeles $(4200
\mathrm{km})$.
Problem 26
By expressing \(\epsilon_{0}\) and \(\mu_{0}\) in base SI units $(\mathrm{kg},
\mathrm{m}, \mathrm{s}, \mathrm{A})$ prove that the only combination of the
two with dimensions of speed is $\left(\boldsymbol{\epsilon}_{0}
\mu_{0}\right)^{-1 / 2}$.
Problem 27
The electric field in a microwave traveling through air has amplitude $0.60
\mathrm{mV} / \mathrm{m}\( and frequency \)30 \mathrm{GHz}$. Find the amplitude
and frequency of the magnetic field.
Problem 28
The magnetic field in a microwave traveling through vacuum has amplitude $4.00
\times 10^{-11} \mathrm{T}\( and frequency \)120 \mathrm{GHz}$. Find the
amplitude and frequency of the electric field.
Problem 29
The magnetic field in a radio wave traveling through air has amplitude $2.5
\times 10^{-11} \mathrm{T}\( and frequency \)3.0 \mathrm{MHz}$. (a) Find the
amplitude and frequency of the electric field. (b) The wave is traveling in
the \(-y\) -direction. At \(y=0\) and \(t=0\), the magnetic field is $1.5 \times
10^{-11} \mathrm{T}\( in the \)+z$ -direction. What are the magnitude and
direction of the electric field at \(y=0\) and \(t=0 ?\)
Problem 30
The electric field in a radio wave traveling through vacuum has amplitude $2.5
\times 10^{-4} \mathrm{V} / \mathrm{m}\( and frequency \)1.47 \mathrm{MHz}$.
(a) Find the amplitude and frequency of the magnetic field. (b) The wave is
traveling in the \(+x\) -direction. At \(x=0\) and \(t=0,\) the electric field is
\(1.5 \times 10^{-4} \mathrm{V} / \mathrm{m}\) in the
\- y-direction. What are the magnitude and direction of the magnetic field at
\(x=0\) and \(t=0 ?\).
Problem 31
The magnetic field of an EM wave is given by \(B_{y}=\) $B_{\mathrm{m}} \sin (k
z+\omega t), B_{x}=0,\( and \)B_{z}=0 .$ (a) In what direction is this wave
traveling? (b) Write expressions for the components of the electric field of
this wave.
Problem 32
The electric field of an EM wave is given by \(E_{z}=\) $E_{\mathrm{m}} \sin (k
y-\omega t+\pi / 6), E_{x}=0,\( and \)E_{z}=0 .$ (a) In what direction is this
wave traveling? (b) Write expressions for the components of the magnetic field
of this wave.
Problem 34
The intensity of the sunlight that reaches Earth's upper atmosphere is approximately \(1400 \mathrm{W} / \mathrm{m}^{2} .\) (a) What is the average energy density? (b) Find the rms values of the electric and magnetic fields.
Problem 35
The cylindrical beam of a 10.0 -mW laser is \(0.85 \mathrm{cm}\) in diameter. What is the rms value of the electric field?
