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Chapter 31: Problem 63

What is the distance between successive heating antinodes in a microwave oven's cavity? A microwave oven typically operates at a frequency of \(2.4 \mathrm{GHz}\).

Short Answer

Expert verified
Answer: The distance between successive heating antinodes in a microwave oven's cavity is approximately 6.25 cm.

Step by step solution

01

Determine the Wavelength

To find the wavelength (λ), we can use the equation: $$ \lambda = \frac{c}{f} $$ where c is the speed of light (\(3.0 \times 10^{8} \mathrm{m/s}\)) and f is the given frequency (\(2.4 \times 10^9 \mathrm{Hz}\) or \(2.4 \mathrm{GHz}\)).
02

Calculate the Wavelength

Now, we can plug the values of c and f into the equation from Step 1 to find the wavelength: $$ \lambda = \frac{3.0 \times 10^8 \mathrm{m/s}}{2.4 \times 10^9 \mathrm{Hz}} = \frac{3.0}{2.4} \times 10^{-1} \mathrm{m} = 1.25 \times 10^{-1} \mathrm{m} $$ So the wavelength of the microwaves is \(0.125 \mathrm{m}\) or \(12.5 \mathrm{cm}\).
03

Find the Distance Between Successive Antinodes

Since there are two antinodes within one complete wavelength and the distance between two successive antinodes is half of the wavelength, we can find the distance between the antinodes as follows: $$ D = \frac{\lambda}{2} = \frac{1.25 \times 10^{-1} \mathrm{m}}{2} = 0.625 \times 10^{-1} \mathrm{m} = 6.25 \mathrm{cm} $$ Therefore, the distance between successive heating antinodes in a microwave oven's cavity is approximately \(6.25 \mathrm{cm}\).

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Most popular questions from this chapter

Which of the following exerts the largest amount of radiation pressure? a) a \(1-\mathrm{mW}\) laser pointer on a \(2-\mathrm{mm}\) -diameter spot \(1 \mathrm{~m}\) away b) a 200-W light bulb on a 4 -mm-diameter spot \(10 \mathrm{~m}\) away c) a 100 -W light bulb on a 2 -mm-diameter spot 4 m away d) a 200 - \(\mathrm{W}\) light bulb on a 2 -mm-diameter spot \(5 \mathrm{~m}\) away e) All of the above exert the same pressure.

The wavelength range for visible light is \(400 \mathrm{nm}\) to \(700 \mathrm{nm}\) (see Figure 31.10 ) in air. What is the frequency range of visible light?

A wire of radius \(1.0 \mathrm{~mm}\) carries a current of 20.0 A. The wire is connected to a parallel plate capacitor with circular plates of radius \(R=4.0 \mathrm{~cm}\) and a separation between the plates of \(s=2.0 \mathrm{~mm} .\) What is the magnitude of the magnetic field due to the changing electric field at a point that is a radial distance of \(r=1.0 \mathrm{~cm}\) from the center of the parallel plates? Neglect edge effects.

A monochromatic point source of light emits \(1.5 \mathrm{~W}\) of electromagnetic power uniformly in all directions. Find the Poynting vector at a point situated at each of the following locations: a) \(0.30 \mathrm{~m}\) from the source b) \(0.32 \mathrm{~m}\) from the source c) \(1.00 \mathrm{~m}\) from the source

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.
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