The electromagnetic wave that delivers a cellular phone call to a car has a magnetic field with an rms value of 2.1 x 10-10 T. The wave passes perpendicularly through an open window, the area of which is 0.19 m². How much energy does this wave carry through the window during a 60-s phone call? Ilmite

The electromagnetic wave that delivers a cellular phone call to a car has a magnetic field with an rms value of 2.1 x 10-10 T. The wave passes perpendicularly through an open window, the area of which is 0.19 m². How much energy does this wave carry through the window during a 60-s phone call? Ilmite

Principles of Physics: A Calculus-Based Text

5th Edition

ISBN:9781133104261

Author:Raymond A. Serway, John W. Jewett

Publisher:Raymond A. Serway, John W. Jewett

Chapter24: Electromagnetic Waves

Section: Chapter Questions

Problem 2P

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During normal bee?ng, the heat creates a maximum 4.00mv potential across 0.300 m of a person’s chest, creating a 1.00-Hz electromagnetic wave. (a) What is the maximum electric field strength created? (b) What is the corresponding maximum magnetic field strength in the electromagnetic wave? (c) What is the wavelength of the electromagnetic wave?
Unreasonable Results A researcher measures the wavelength of a 1.20-GHz electromagnetic wave to be 0.500 m. (a) Calculate the speed at which this wave propagates. (b) What is unreasonable about this result? (c) Which assumptions are unreasonable or inconsistent?
Consider an electromagnetic wave traveling in the positive y direction. The magnetic field associated with the wave at some location at some instant points in the negative x direction as shown in Figure OQ24.12. What is the direction of the electric field at this position and at this instant? (a) the positive x direction (b) the positive y direction (c) the positive z direction (d) the negative z direction (e) the negative y direction Figure OQ24.12
A dish antenna having a diameter of 20.0 m receives (at normal incidence) a radio signal from a distant source as shown in Figure P24.63. The radio signal is a continuous sinusoidal wave with amplitude Emax = 0.200 V/m. Assume the antenna absorbs all the radiation that falls on the dish. (a) What is the amplitude of the magnetic field in this wave? (b) What is the intensity of the radiation received by this antenna? (c) What is the power received by the antenna? (d) What force is exerted by the radio waves on the antenna? Figure P24.63
Review. Model the electromagnetic wave in a microwave oven as a plane traveling wave moving to the left, with an intensity of 25.0 kW/m2. An oven contains two cubical containers of small mass, each full of water. One has an edge length of 6.00 cm, and the other, 12.0 cm. Energy falls perpendicularly on one face of each container. The water in the smaller container absorbs 70.0% of the energy that falls on it. The water in the larger container absorbs 91.0%. That is, the fraction 0.300 of the incoming microwave energy passes through a 6.00-cm thickness of water, and the fraction (0.300)(0.300) = 0.090 passes through a 12.0-cm thickness. Assume a negligible amount of energy leaves either container by heat. Find the temperature change of the water in each container over a time interval of 480 s.
You may wish to review Sections 16.4 and 16.8 on the transport of energy by string waves and sound. Figure P33.46 is a graphical representation of an electromagnetic wave moving in the x direction. We wish to find an expression for the intensity of this wave by means of a different process from that by which Equation 33.27 was generated. (a) Sketch a graph of the electric field in this wave at the instant t = 0, letting your flat paper represent the xy plane. (b) Compute the energy density uE in the electric field as a function of x at the instant t = 0. (c) Compute the energy density in the magnetic field uB as a function of x at that instant. (d) Find the total energy density u as a function of x, expressed in terms of only the electric field amplitude. (e) The energy in a shoebox of length and frontal area A is E=0uAdx. (The symbol E for energy in a wavelength imitates the notation of Section 16.4.) Perform the integration to compute the amount of this energy in terms of A, , Emax, and universal constants. (f) We may think of the energy transport by the whole wave as a series of these shoeboxes going past as if carried on a conveyor belt. Each shoebox passes by a point in a time interval defined as the period T = 1/f of the wave. Find the power the wave carries through area A. (g) The intensity of the wave is the power per unit area through which the wave passes. Compute this intensity in terms of Emax and universal constants. (h) Explain how your result compares with that given in Equation 33.27. Figure P33.46
A particle of cosmic dust has a density =2.0g/cm3 , (a) Assuming the dust particles are spherical and light absorbing, and are at the same distance as Earth from the Sun, determine the particle size for which radiation pressure from sunlight is equal to the Sun's force of gravity on the dust particle, (b) Explain how the forces compare if the particle radius is smaller, (c) Explain what this implies about the sizes of dust particle likely to be present in the inner solar system compared with outside the Oort cloud.
Lasers can be constructed that produce an extremely high intensity electromagnetic wave for a brief time—called pulsed lasers. They are used to initiate nuclear fusion, for example. Such a laser may produce an electromagnetic wave with a maximum electric field strength of 1.001011 V/m for a time of 1.00 ns. (a) What is the maximum magnetic field strength in the wave? (b) What is the intensity of the beam? (c) What energy does it deliver on an 1.00-mm2 area?
Review. Consider a capacitor with vacuum between its large, closely spaced, oppositely charged parallel plates. (a) Show that the force on one plate can be accounted for by thinking of the electric field between the plates as exerting a negative pressure equal to the energy density of the electric field. (b) Consider two infinite plane sheets carrying electric currents in opposite directions with equal linear current densities Js. Calculate the force per area acting on one sheet due to the magnetic field, of magnitude 0Js/2, created by the other sheet. (c) Calculate the net magnetic field between the sheets and the field outside of the volume between them. (d) Calculate the energy density in the magnetic field between the sheets. (e) Show that the force on one sheet can be accounted for by thinking of the magnetic field between the sheets as exerting a positive pressure equal to its energy density. This result for magnetic pressure applies to all current configurations, not only to sheets of current.
A spherical interplanetary grain of dust of radius 0.2 m is at a distance r1 from the Sun. The gravitational force exerted by the Sun on the grain just balances the force due to radiation pressure from the Sun's light. (i) Assume the grain is moved to a distance 2r1 from the Sun and released. At this location, what is the net force exerted on the grain? (a) toward the Sun (b) away from the Sun (c) zero (d) impossible to determine without knowing the mass of the grain (ii) Now assume the grain is moved back to its original location at r1, compressed so that it crystallizes into a sphere with significantly higher density, and then released. In this situation, what is the net force exerted on the grain? Choose from the same possibilities as in part (i).
A large, flat sheet carries a uniformly distributed electric current with current per unit width Js. This current creates a magnetic field on both sides of the sheet, parallel to the sheet and perpendicular to the current, with magnitude B=120Js. If the current is in the y direction and oscillates in time according to Jmax(cost)j=Jmax[cos(t)]j the sheet radiates an electromagnetic wave. Figure P33.28 shows such a wave emitted from one point on the sheet chosen to be the origin. Such electromagnetic waves arc emitted from all points on the sheet. The magnetic field of the wave to the right of the sheet is described by the wave function B=120Jmax[cos(kxt)]k (a) Find the wave function for the electric field of the wave to the right of the sheet. (b) Find the Poynting vector as a function of x and t. (c) Find the intensity of the wave. (d) What If? If the sheet is to emit radiation in each direction (normal to the plane of the sheet) with intensity 570 W/m2, what maximum value of sinusoidal current density is required? Figure P33.28
A very large parallel-plate capacitor has uniform charge per unit area + on the upper plate and on the lower plate. The plates are horizontal, and both move horizontally with speed v to the right. (a) What is the magnetic field between the plates? (b) What is the magnetic field just above or just below the plates? (c) What are the magnitude and direction of the magnetic force per unit area on the upper plate? (d) At what extrapolated speed v will the magnetic force on a plate balance the electric force on the plate? Suggestion: Use Amperes law and choose a path that closes between the plates of the capacitor.