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Chapter 22: Problem 27

The electric field in a microwave traveling through air has amplitude $0.60 \mathrm{mV} / \mathrm{m}\( and frequency \)30 \mathrm{GHz}$. Find the amplitude and frequency of the magnetic field.

Short Answer

Expert verified
Answer: The amplitude of the magnetic field associated with the microwave is 2 * 10^(-12) T, and the frequency is 30 GHz.

Step by step solution

01

Write down the given information

The amplitude of the electric field (E) is 0.60 mV/m and the frequency (f) is 30 GHz.
02

Convert the units to SI units

We need to convert the given values to SI units, so we'll convert mV/m to V/m and GHz to Hz: E = 0.60 * 10^(-3) V/m = 6.0 * 10^(-4) V/m f = 30 * 10^9 Hz
03

Calculate the angular frequency (蠅)

The angular frequency (蠅) is related to the frequency (f) by the following formula: 蠅 = 2蟺f Now, we'll substitute the given frequency into the equation and solve for the angular frequency: 蠅 = 2蟺(30 * 10^9 Hz) = 60蟺 * 10^9 rad/s
04

Calculate the speed of light in the medium (c)

As the microwave is traveling through air, we can assume that the speed of light in the medium is the same as the speed of light in vacuum. Therefore, c = 3 * 10^8 m/s.
05

Calculate the amplitude of the magnetic field (B)

Now that we know the amplitude and angular frequency of the electric field, we can use the following formula to calculate the amplitude of the magnetic field (B): B = E/c Substitute the values of E and c into the equation: B = (6.0 * 10^(-4) V/m) / (3 * 10^8 m/s) = 2 * 10^(-12) T The amplitude of the magnetic field is 2 * 10^(-12) T.
06

Frequency of the magnetic field

In an electromagnetic wave, the frequency of the electric field is the same as the frequency of the magnetic field. Therefore, the frequency of the magnetic field is 30 GHz. The final answer is: the amplitude of the magnetic field is 2 * 10^(-12) T, and the frequency is 30 GHz.

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Most popular questions from this chapter

Unpolarized light is incident on a system of three polarizers. The second polarizer is oriented at an angle of \(30.0^{\circ}\) with respect to the first and the third is oriented at an angle of \(45.0^{\circ}\) with respect to the first. If the light that emerges from the system has an intensity of $23.0 \mathrm{W} / \mathrm{m}^{2},$ what is the intensity of the incident light?
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An electric dipole antenna used to transmit radio waves is oriented vertically.At a point due north of the transmitter, how should a magnetic dipole antenna be oriented to serve as a receiver?
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A magnetic dipole antenna is used to detect an electromagnetic wave. The antenna is a coil of 50 turns with radius \(5.0 \mathrm{cm} .\) The EM wave has frequency \(870 \mathrm{kHz}\) electric field amplitude $0.50 \mathrm{V} / \mathrm{m},\( and magnetic field amplitude \)1.7 \times 10^{-9} \mathrm{T} .$ (a) For best results, should the axis of the coil be aligned with the electric field of the wave, or with the magnetic field, or with the direction of propagation of the wave? (b) Assuming it is aligned correctly, what is the amplitude of the induced emf in the coil? (Since the wavelength of this wave is much larger than \(5.0 \mathrm{cm},\) it can be assumed that at any instant the fields are uniform within the coil.) (c) What is the amplitude of the emf induced in an electric dipole antenna of length \(5.0 \mathrm{cm}\) aligned with the electric field of the wave?
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