Chapter 29: Problem 4
List some similarities and differences between electromagnetic waves and sound waves.
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Chapter 29: Problem 4
List some similarities and differences between electromagnetic waves and sound waves.
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Show that it's impossible for an electromagnetic wave in vacuum to have a time-varying component of its electric field in the direction of its magnetic field. (Hint: Assume \(\vec{E}\) does have such a component, and show that you can't satisfy both Gauss's and Faraday's laws.)
One spacecraft has a sail that absorbs all light incident on it; the other has a perfectly reflective sail. How do their accelerations compare in light with the same intensity? a. The absorptive sail gives twice the acceleration. b. The reflective sail gives twice the acceleration. c. The absorptive sail gives greater acceleration, but not twice as much. d. The reflective sail gives greater acceleration, but not twice as much.
A cylindrical resistor of length \(L\), radius \(a\), and resistance \(R\) carries current \(I\). Calculate the electric and magnetic fields at the surface of the resistor, assuming the electric field is uniform over the surface. Calculate the Pointing vector and show that it points into the resistor. Calculate the flux of the Pointing vector (that is, \(\int \vec{S} \cdot d \vec{A}\) ) over the resistor's surface to get the rate of electromagnetic energy flow into the resistor, and show that the result is \(I^{2} R\) Your result shows that the energy heating the resistor comes from the fields surrounding it. These fields are sustained by the source of electric energy that drives the current.
Maxwell's equations in a dielectric resemble those in vacuum (Equations \(29.6-29.9)\) but with \(\epsilon_{0}\) replaced by \(\kappa \epsilon_{0}\). where \(\kappa\) is the dielectric constant introduced in Chapter \(23 .\) Show that the speed of electromagnetic waves in a electric is \(c / \sqrt{\kappa}\).
You're engineering a new cell phone, and you'd like to incorporate the antenna entirely within the phone, which is \(9 \mathrm{cm}\) long when closed. The antenna is to be a quarter-wavelength long-a common design for vertically oriented antennas. If the cell-phone frequency is \(2.4 \mathrm{GHz}\), will the antenna fit?
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