(a).
The sketch of the graph of electric field for the given wave at time
(a).
Answer to Problem 70AP
The sketch of the graph of electric field for the given wave at time
Explanation of Solution
The sketch the graph of electric field for the given wave at time
Figure-(1)
(b).
The energy density in the electric field as a function of
(b).
Answer to Problem 70AP
The energy density in the electric field as a function of
Explanation of Solution
Write the equation for the electric field varying in
Here,
Write the expression for the energy density in terms of electric field.
Here,
Substitute
Conclusion:
Substitute
Therefore, the energy density in the electric field as a function of
(c).
The energy density in the magnetic field as a function of
(c).
Answer to Problem 70AP
The energy density in the magnetic field as a function of
Explanation of Solution
Write the equation for the magnetic field varying in
Here,
Write the expression for the energy density in terms of magnetic field.
Here,
Substitute
Conclusion:
Substitute
Therefore, the energy density in the magnetic field as a function of
(d).
The total energy density as a function of
(d).
Answer to Problem 70AP
The total energy density as a function of
Explanation of Solution
Write the expression for the total energy density.
Substitute
Write the relation between the electric and the magnetic field.
Substitute
Substitute
Therefore, the total energy density as a function of
(e).
The energy in the "shoebox" in terms of
(e).
Answer to Problem 70AP
The energy in the "shoebox" in terms of
Explanation of Solution
Write the given equation for energy.
Here,
Substitute
Write the expression for the wave vector.
Substitute
`
Therefore, the energy in the "shoebox" in terms of
(f).
The power the wave carries through the area
(f).
Answer to Problem 70AP
The power the wave carries through the area
Explanation of Solution
Write the expression for power through an area
Here,
Substitute
Also,
Here,
Substitute
Therefore, the power the wave carries through the area
(g).
The intensity in terms of
(g).
Answer to Problem 70AP
The intensity in terms of
Explanation of Solution
Write the expression for intensity.
Here,
Substitute
Also,
Substitute
Therefore, the intensity in terms of
(h).
The comparison of the result in part
(h).
Answer to Problem 70AP
On comparison of equation (XVIII) and (XIX), both the equation yields the same result for the intensity. Therefore, the intensity is same for both the conditions.
Explanation of Solution
The equation (34.24) is,
The result obtained in part
On comparison of equation (XVIII) and (XIX), both the equation yields the same result for the intensity. Therefore, the intensity is same for both the conditions.
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Chapter 34 Solutions
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