Log out Go to App
Go to App

Learning Materials

Features

Discover

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 (ω)

The angular frequency (ω) is related to the frequency (f) by the following formula: ω = 2πf Now, we'll substitute the given frequency into the equation and solve for the angular frequency: ω = 2π(30 * 10^9 Hz) = 60π * 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.

Unlock Step-by-Step Solutions & Ace Your Exams!

  • Full Textbook Solutions

    Get detailed explanations and key concepts

  • Unlimited Al creation

    Al flashcards, explanations, exams and more...

  • Ads-free access

    To over 500 millions flashcards

  • Money-back guarantee

    We refund you if you fail your exam.

Start your free trial

Over 30 million students worldwide already upgrade their learning with Vaia!

One App. One Place for Learning.

All the tools & learning materials you need for study success - in one app.

Get started for free

Most popular questions from this chapter

A police car's radar gun emits microwaves with a frequency of $f_{1}=36.0 \mathrm{GHz}$. The beam reflects from a speeding car, which is moving away at \(43.0 \mathrm{m} / \mathrm{s}\) with respect to the police car. The frequency of the reflected microwave as observed by the police is \(f_{2} .\) (a) Which is larger, \(f_{1}\) or \(f_{2} ?\) (b) Find the frequency difference \(f_{2}-f_{1}\) [Hint: There are two Doppler shifts. First think of the police as source and the speeder as observer. The speeding car "retransmits" a reflected wave at the same frequency at which it observes the incident wave. \(]\)
The magnetic field of an EM wave is given by \(B_{y}=\) $B_{\mathrm{m}} \sin (k z+\omega t), B_{x}=0,\( and \)B_{z}=0 .$ (a) In what direction is this wave traveling? (b) Write expressions for the components of the electric field of this wave.
Calculate the frequency of an EM wave with a wavelength the size of (a) the thickness of a piece of paper \((60 \mu \mathrm{m}),(\mathrm{b})\) a \(91-\mathrm{m}\) -long soccer field, (c) the diameter of Earth, (d) the distance from Earth to the Sun.
Just after sunrise, you look north at the sky just above the horizon. Is the light you see polarized? If so, in what direction?
The intensity of solar radiation that falls on a detector on Earth is $1.00 \mathrm{kW} / \mathrm{m}^{2} .\( The detector is a square that measures \)5.00 \mathrm{m}$ on a side and the normal to its surface makes an angle of \(30.0^{\circ}\) with respect to the Sun's radiation. How long will it take for the detector to measure \(420 \mathrm{kJ}\) of energy?
See all solutions

Recommended explanations on Physics Textbooks

Kinematics Physics

Read Explanation

Atoms and Radioactivity

Read Explanation

Mechanics and Materials

Read Explanation

Wave Optics

Read Explanation

Torque and Rotational Motion

Read Explanation

Scientific Method Physics

Read Explanation
View all explanations

What do you think about this solution?

We value your feedback to improve our textbook solutions.

Study anywhere. Anytime. Across all devices.

Sign-up for free