Log out Go to App
Go to App

Learning Materials

Features

Discover

Chapter 31: Q. 8 (page 900)

The intensity of an electromagnetic wave is 10W/m2. What will the intensity be if:

a. The amplitude of the electric field is doubled?

b. The amplitude of the magnetic field is doubled?

c. The amplitudes of both the electric and the magnetic fields are doubled?

d. The frequency is doubled?

Short Answer

Expert verified

(a) Since I∝E02, the new intensity is40W/m2

(b) For an electromagnetic waveE0∝B0, so 40W/m2.

(c) When it comes to electromagnetic waves, increasing one amplitude necessitates doubling the other, so 40W/m2.

(d) Since the amplitudes are unaffected by changing the frequency, the intensity remains constant at 10W/m2.

Step by step solution

01

Amplitude of electric field

The energy crossing per second per unit area parallel to the direction of propagation of electromagnetic waves is defined as the intensity of electromagnetic waves. where c is the electromagnetic wave's velocity.

02

Energy in Electromagnetic waves

The energy of such a wave is proportional of its amplitude (E2 or B2). This really is valid for waves on strings, water waves, and sound waves, where amplitude and pressure are proportional. The maximum field strength of the electric and magnetic is the amplitude in electromagnetic waves.

As a conclusion, the energy carried by such an electromagnetic wave and also its intensity Iis proportional to E2and B2.In fact, the increasing quality wave of such a continuous oscillatory electromagnetic field is given by

Iave=cϵ0E022

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

You've recently read about a chemical laser that generates a 20-cm-diameter,25MW laser beam. One day, after physics class, you start to wonder if you could use the radiation pressure from this laser beam to launch small payloads into orbit. To see if this might be feasible, you do a quick calculation of the acceleration of a 20-cm-diameter, 100kg, perfectly absorbing block. What speed would such a block have if pushed horizontally 100m along a frictionless track by such a laser?

The magnetic field inside a 4.0-cm-diameter superconducting solenoid varies sinusoidally between 8.0T and 12.0Tat a frequency of 10Hz.

a. What is the maximum electric field strength at a point 1.5cmfrom the solenoid axis?

b. What is the value of B at the instant E reaches its maximum value?

In FIGURE P31.33, a circular loop of radius rtravels with speed valong a charged wire having linear charge density I. The wire is at rest in the laboratory frame, and it passes through the center of the loop.

a. What are E→and B→at a point on the loop as measured by a scientist in the laboratory? Include both strength and direction.

b. What are the fields E→and B→at a point on the loop as measured by a scientist in the frame of the loop?

c. Show that an experimenter in the loop’s frame sees a currentI=λνpassing through the center of the loop.

d. What electric and magnetic fields would an experimenter in the loop’s frame calculate at distance r from the current of part c?

e. Show that your fields of parts b and d are the same.

A proton is fired with a speed of 1.0×106m/sthrough the parallel-plate capacitor shown in FIGURE P31.31. The capacitor's electric field is role="math" localid="1648984502437" E→=1.0×105V/m,down).

a. What magnetic field B→, both strength and direction, must be applied to allow the proton to pass through the capacitor with no change in speed or direction?

b. Find the electric and magnetic fields in the proton's reference frame.

c. How does an experimenter in the proton's frame explain that the proton experiences no force as the charged plates fly by?

a. Show that uEand uB, the energy densities of the electric and magnetic fields, are equal to each other in an electromagnetic wave. In other words, show that the wave’s energy is divided equally between the electric field and the magnetic field.

b. What is the total energy density in an electromagnetic wave of intensity 1000W/m2?
See all solutions

Recommended explanations on Physics Textbooks

Geometrical and Physical Optics

Read Explanation

Modern Physics

Read Explanation

Electric Charge Field and Potential

Read Explanation

Conservation of Energy and Momentum

Read Explanation

Fundamentals of Physics

Read Explanation

Oscillations

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