Warning: foreach() argument must be of type array|object, bool given in /var/www/html/web/app/themes/studypress-core-theme/template-parts/header/mobile-offcanvas.php on line 20

A sinusoidal electromagnetic wave emitted by a cellular phone has a wavelength of 35.4 cm and an electric-field amplitude of5.40×10-2V/m at adistance of 250 m from the phone. Calculate (a) the frequency of the wave; (b) the magnetic-field amplitude; (c) the intensity of the wave.

Short Answer

Expert verified

a. The frequency of wave is 8.74×108Hz.

b. The amplitude of magnetic-field is 1.8×10-10T.

c. The intensity of wave is 3.87×10-6W/m2.

Step by step solution

01

Define the intensity ( I ) and the formulas.

The power transported per unit area is known as the intensity ( I ).

The formula used to calculate the intensity( I ) is:

I=PA

Where,A is area measured in the direction perpendicular to the energy andP is the power in watts.

The relation between the frequency of wave f, wavelengthλ and speed of lightc is:

c=fλ

And also, I=12ε0cEmax2 . Where, I is the intensity in W/m2and is the speed of light that is equal to 3.0×108m/sand ε0=8.85×10-12C2/N·m2.

The relation between the maximum electric field and maximum magnetic field is:

Bmax=Emaxc

02

Determine frequency of wave.

Given that,λ=35.4×10-2m

The frequency of wave is:

f=cλ=3×10835.4×10-2=8.47×108Hz

Hence, the frequency of wave is 8.47×108Hz.

03

Determine the amplitude of magnetic field.

Given that,Emax=5.4×10-2V/m

The amplitude of magnetic field is:

Bmax=Emaxc=5.4×10-23×108=1.8×10-10T

Hence, the amplitude of magnetic-field is 1.8×10-10T.

04

Determine the intensity of wave.

The intensity of wave:

I=12ε0cEmax2=12×8.854×10-123×1085.4×10-2=3.87×10-6W/m2

Hence, intensity of wave is 3.87×10-6W/m2.

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.

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

Ordinary household electric lines in North America usually operate at 120 V . Why is this a desirable voltage, rather than a value considerably larger or smaller? On the other hand, automobiles usually have 12 V electrical systems. Why is this a desirable voltage?

When is a 1.5 - VAAA battery not actually a 1.5 - V battery? That is, when do this its terminals provide a potential difference of less than 1.5 V ?

An idealized voltmeter is connected across the terminals of a15.0-Vbattery, and arole="math" localid="1655719696009" 75.0-Ω appliance is also connected across its terminals. If the voltmeter reads11.9V (a) how much power is being dissipated by the appliance, and (b) what is the internal resistance of the battery?

A typical small flashlight contains two batteries, each having an emf of1.5V, connected in series with a bulb having resistance17Ω. (a) If the internal resistance of the batteries is negligible, what power is delivered to the bulb? (b) If the batteries last for1.5hwhat is the total energy delivered to the bulb? (c) The resistance of real batteries increases as they run down. If the initial internal resistance is negligible, what is the combined internal resistance of both batteries when the power to the bulb has decreased to half its initial value? (Assume that the resistance of the bulb is constant. Actually, it will change somewhat when the current through the filament changes, because this changes the temperature of the filament and hence the resistivity of the filament wire.)

A 5.00-A current runs through a 12-gauge copper wire (diameter

2.05 mm) and through a light bulb. Copper has8.5×108free electrons per

cubic meter. (a) How many electrons pass through the light bulb each

second? (b) What is the current density in the wire? (c) At what speed does

a typical electron pass by any given point in the wire? (d) If you were to use

wire of twice the diameter, which of the above answers would change?

Would they increase or decrease?

See all solutions

Recommended explanations on Physics Textbooks

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