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Chapter 31: Problem 2

Which of the following statements concerning electromagnetic waves are incorrect? (Select all that apply.) a) Electromagnetic waves in vacuum travel at the speed of light. b) The magnitudes of the electric field and the magnetic field are equal. c) Only the electric field vector is perpendicular to the direction of the wave's propagation. d) Both the electric field vector and the magnetic field vector are perpendicular to the direction of propagation. e) An electromagnetic wave carries energy only when \(E=B\).

Short Answer

Expert verified
a) Electromagnetic waves in a vacuum travel at the speed of light. b) The magnitudes of the electric field and magnetic field are equal. c) Only the electric field vector is perpendicular to the direction of the wave's propagation. d) Both the electric field vector and the magnetic field vector are perpendicular to the direction of propagation. e) An electromagnetic wave carries energy only when the magnitudes E and B are equal. Answer: The incorrect statements concerning electromagnetic waves are (b), (c), and (e).

Step by step solution

01

Understand properties of electromagnetic waves

Electromagnetic waves are disturbances created in both the electric and magnetic fields that propagate through space. Some key properties to remember are: 1. Electromagnetic waves in a vacuum travel at the speed of light (\(c\)). 2. The electric field vector (\(\vec{E}\)) and the magnetic field vector (\(\vec{B}\)) are always perpendicular to each other and to the direction of propagation. Now let's analyze each statement to identify the incorrect ones.
02

Analyze statement (a)

Statement (a) says that electromagnetic waves in vacuum travel at the speed of light. This statement is correct, as it matches the first key property of electromagnetic waves mentioned above.
03

Analyze statement (b)

Statement (b) claims that the magnitudes of the electric field and magnetic field are equal. This statement is not necessarily true, as the magnitudes of the electric field and magnetic field can vary depending on the medium and polarization. So, statement (b) is incorrect.
04

Analyze statement (c)

Statement (c) says that only the electric field vector is perpendicular to the direction of the wave's propagation. This statement is incorrect because, as mentioned in step 1, both the electric field vector and the magnetic field vector are perpendicular to the direction of propagation.
05

Analyze statement (d)

Statement (d) states that both the electric field vector and the magnetic field vector are perpendicular to the direction of propagation. This statement is correct and matches the second key property mentioned in step 1.
06

Analyze statement (e)

Statement (e) claims that an electromagnetic wave carries energy only when the magnitudes \(E\) and \(B\) are equal. This statement is incorrect because the energy carried by an electromagnetic wave is the product of the magnitudes of electric field (\(E\)) and magnetic field (\(B\sin\theta\)), where \(\theta\) is the angle between the electric field vector and magnetic field vector. Such a product doesn't require equal magnitudes of \(E\) and \(B\).
07

Identify the incorrect statements

Based on the above discussion, the incorrect statements concerning electromagnetic waves are (b), (c), and (e).

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Most popular questions from this chapter

.An industrial carbon dioxide laser produces a beam of radiation with average power of \(6.00 \mathrm{~kW}\) at a wavelength of \(10.6 \mu \mathrm{m}\). Such a laser can be used to cut steel up to \(25 \mathrm{~mm}\) thick. The laser light is polarized in the \(x\) -direction, travels in the positive \(z\) -direction, and is collimated (neither diverging or converging) at a constant diameter of \(100.0 \mu \mathrm{m} .\) Write the equations for the laser light's electric and magnetic fields as a function of time and of position \(z\) along the beam. Recall that \(\vec{E}\) and \(\vec{B}\) are vectors. Leave the overall phase unspecified, but be sure to check the relative phase between \(\vec{E}\) and \(\vec{B}\) .

Quantum theory says that electromagnetic waves actually consist of discrete packets-photons-each with energy \(E=\hbar \omega,\) where \(\hbar=1.054573 \cdot 10^{-34} \mathrm{~J} \mathrm{~s}\) is Planck's reduced constant and \(\omega\) is the angular frequency of the wave. a) Find the momentum of a photon. b) Find the angular momentum of a photon. Photons are circularly polarized; that is, they are described by a superposition of two plane-polarized waves with equal field amplitudes, equal frequencies, and perpendicular polarizations, one-quarter of a cycle \(\left(90^{\circ}\right.\) or \(\pi / 2\) rad \()\) out of phase, so the electric and magnetic field vectors at any fixed point rotate in a circle with the angular frequency of the waves. It can be shown that a circularly polarized wave of energy \(U\) and angular frequency \(\omega\) has an angular momentum of magnitude \(L=U / \omega .\) (The direction of the angular momentum is given by the thumb of the right hand, when the fingers are curled in the direction in which the field vectors circulate. c) The ratio of the angular momentum of a particle to \(\hbar\) is its spin quantum number. Determine the spin quantum number of the photon.

Three FM radio stations covering the same geographical area broadcast at frequencies \(91.1,91.3,\) and \(91.5 \mathrm{MHz},\) respectively. What is the maximum allowable wavelength width of the band-pass filter in a radio receiver so that the FM station 91.3 can be played free of interference from FM 91.1 or FM 91.5? Use \(c=3.00 \cdot 10^{8} \mathrm{~m} / \mathrm{s}\), and calculate the wavelength to an uncertainty of \(1 \mathrm{~mm} .\)

A \(5.00-\mathrm{mW}\) laser pointer has a beam diameter of \(2.00 \mathrm{~mm}\) a) What is the root-mean-square value of the electric field in this laser beam? b) Calculate the total electromagnetic energy in \(1.00 \mathrm{~m}\) of this laser beam.

Scientists have proposed using the radiation pressure of sunlight for travel to other planets in the Solar System. If the intensity of the electromagnetic radiation produced by the Sun is about \(1.40 \mathrm{~kW} / \mathrm{m}^{2}\) near the Earth, what size would a sail have to be to accelerate a spaceship with a mass of 10.0 metric tons at \(1.00 \mathrm{~m} / \mathrm{s}^{2} ?\) a) Assume that the sail absorbs all the incident radiation. b) Assume that the sail perfectly reflects all the incident radiation.
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