Chapter 31: Problem 64
What is the electric field amplitude of an electromagnetic wave whose magnetic field amplitude is \(5.00 \cdot 10^{-3} \mathrm{~T} ?\)
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Two polarizers are out of alignment by \(30.0^{\circ} .\) If light of intensity \(1.00 \mathrm{~W} / \mathrm{m}^{2}\) and initially polarized halfway between the polarizing angles of the two filters passes through both filters, what is the intensity of the transmitted light?
The most intense beam of light that can propagate through dry air must have an electric field whose maximum amplitude is no greater than the breakdown value for air: \(E_{\max }^{\text {air }}=3.0 \cdot 10^{6} \mathrm{~V} / \mathrm{m}\), assuming that this value is unaffected by the frequency of the wave. a) Calculate the maximum amplitude the magnetic field of this wave can have. b) Calculate the intensity of this wave. c) What happens to a wave more intense than this?
Two polarizing filters are crossed at \(90^{\circ}\), so when light is shined from behind the pair of filters, no light passes through. A third filter is inserted between the two, initially aligned with one of them. Describe what happens as the intermediate filter is rotated through an angle of \(360^{\circ}\)
A microwave operates at \(250 .\) W. Assuming that the waves emerge from a point source emitter on one side of the oven, how long does it take to melt an ice cube \(2.00 \mathrm{~cm}\) on a side that is \(10.0 \mathrm{~cm}\) away from the emitter if \(10.0 \%\) of the photons that strike the cube are absorbed by it? How many photons of wavelength \(10.0 \mathrm{~cm}\) hit the ice cube per second? Assume a cube density of \(0.960 \mathrm{~g} / \mathrm{cm}^{3}\)
A voltage, \(V\), is applied across a cylindrical conductor of radius \(r\) length \(L,\) and resistance \(R .\) As a result, a current, \(i,\) is flowing through the conductor, which gives rise to a magnetic field, \(B\). The conductor is placed along the \(y\) -axis, and the current is flowing in the positive \(y\) -direction. Assume that the electric field is uniform throughout the conductor. a) Find the magnitude and the direction of the Poynting vector at the surface of the conductor of the static electric and magnetic fields. b) Show that \(\int \vec{S} \cdot d \vec{A}=i^{2} R\)
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