Chapter 29: Problem 21
If you speak via radio from Earth to an astronaut on the Moon, how long is it before you can get a reply?
Chapter 29: Problem 21
If you speak via radio from Earth to an astronaut on the Moon, how long is it before you can get a reply?
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Get started for freeYour roommate's father is CEO of a coal company, so your roommate is understandably skeptical of alternative energy proposals. He claims that there's no future for solar energy, because the power in sunlight is insufficient to meet humankind's energy demand. Is he right? To find out, compare the solar power incident on Earth with our human energy consumption rate of about 15 TW.
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 Poynting vector and show that it points into the resistor. Calculate the flux of the Poynting vector (that is, \(\sqrt{S} \cdot d \vec{A}\) ) 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.
The fields of an electromagnetic wave are \(\vec{E}=E_{p} \sin (k z+\omega t) \hat{\jmath}\) and \(\vec{B}=B_{p} \sin (k z+\omega t) \hat{\imath} .\) Give a unit vector in the wave's propagation direction.
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?
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 dielectric is \(c / \sqrt{\kappa}\).
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