Prove, for a plane electromagnetic wave that is normally incident on a flat surface, that the radiation pressure on the surface is equal to the energy density in the incident beam. (This relation between pressure and energy density holds no matter what fraction of the incident energy is reflected.)

Prove, for a plane electromagnetic wave that is normally incident on a flat surface, that the radiation pressure on the surface is equal to the energy density in the incident beam. (This relation between pressure and energy density holds no matter what fraction of the incident energy is reflected.)

University Physics Volume 2

18th Edition

ISBN:9781938168161

Author:OpenStax

Publisher:OpenStax

Chapter16: Electromagnetic Waves

Section: Chapter Questions

Problem 13CQ: Why is t1 radiation pressure of an electromagnetic wave on a perfectly reflecting surface twice as...

See similar textbooks

Similar questions

A plane electromagnetic wave of frequency 20 GHz moves in the positive y-axis direction such that its electric field is pointed along the z-axis. The amplitude of the electric field is 10 V/m. The start of time is chosen so thatat t = 0 , the electric field has a value 10 V/m at the origin. (a) Write the wave function that will describe the electric field wave. (b) Find the wave function that will describe the associated magnetic field wave.
(a) A linearly polarized electromagnetic waye with polarization normal to the plane of incidence is incident obliquely on a dielectric medium of relative permittivity e,. Find the reflected (E,) and transmitted (E) wave amplitude as a function of the incidence angle 6. Plot schematically the reflection coefficient as a function of the incidence angle 0 for the cases E, 1.
(a) The magnetic field intensity H of an electromagnetic wave propagating in free space in the z-direction is described in phasor form by H = îH¸e¯i where B is its phase constant. Determine the corresponding electric field from Ampere's law. A long straight wire in air carries a current of 5 A. What is the magnetic field intensity H at a radial distance of 5 m from the wire? (b) A battery of open circuit voltage 2 V and internal resistance 50 2 is connected via a rapid switch to a transmission line of characteristic impedance 50 N terminated in a load of 100 N. Calculate the voltage and current on the line just after the switch is closed, explaining your answer carefully. (c)
Consider a sinnsoidal plane electromagnetic wave propagating in -y direction in vacuum. If the amplitude of the electric field component of the wave is (12 V/m)k, what is the magnitude and the direction of the maguetic field component?
A time-harmonic electromagnetic wave with the electric field E = a, 5sin (ot-0.5x) propagates in a lossless dielectric medium of ɛ = 2.0 € u=4, (free of sources). %3D (a) Find the complex phasor representation E of the electric field. (b) Find the complex magnetic field H, using Faraday's law for time-harmonic fields. Write down the magnetic field in real time, H(x,t). D'a low for time.harmonic fi
Find and describe the electromagnetic field produced by a superposition of twoequal-amplitude, monochromatic, plane waves that propagate in opposite directions.(a) Let the wave propagating along +z have left circular polarization and the wavepropagating along −z have right circular polarization.(b) Repeat when both waves have left circular polarization.
When electromagnetic radiation strikes perpendicular to a flat surface, a totally absorbing surface feels radiation pressure I0/c, where I0 is the intensity of incident electromagnetic radiation. A totally reflecting surface feels twice that pressure. More generally, a surface absorbs a proportion e of the incident radiation and reflects a complementary proportion, 1 - e, where e is the emissivity of the surface. Note that 0 ≤ e ≤ 1. (a) Determine the radiation pressure prad in terms of I0 and e. (b) Consider cosmic dust particles in outer space at a distance of 1.5 x 1011 m from the sun, where Isun = 1.4 kW/m2 . We can model these particles as tiny disks with e = 0.61, diameter 8.0 µm and mass 1.0 x 10-10 grams, all oriented perpendicular to the sun’s rays. What is the force on one of these particles that is exerted by the radiation from the sun? (c) What is the ratio of this force to the attractive force of gravity exerted by the sun on the particle?
(a) The electric field of an electromagnetic wave propagating in free space is described by the equation E(z, t) = Eo[Êsin(kz – wt) + ŷcos(kz – wt)] where x and y are unit vectors in the x- and y-direction, respectively. What is this wave's direction of propagation? What is the polarization of the wave? (b) State and prove the boundary conditions satisfied by the magnetic intensity H and the magnetic field B at the boundary between two media with different magnetic properties. (c) Show that tan 01 tan 02 where 0, and 0 , are incident and refraction angles.
(a) A Block of mass 0.2kg is given an initial speed vo =5km/s on a horizontal rough surface of length 2m as in figure. The coefficient of kinetic friction on the horizontal surface is 0.30. if the curved part of the track is frictionless how high does the block rise before coming to rest. 2m (b) Define the Electromagnetic wave, and list various types of it.
A plane electromagnetic wave has an intensity of 750W/m2. A flat, rectangular surface of dimensions 50 cm x 100 cm is placed perpendicular to the direction of the wave. The surface absorbs half of the energy and reflects half. Calculate (a) the total energy absorbed by the surface in 1.00 min and (b) the momentum absorbed in this time.
A thin, totally absorbing sheet of mass m, face area A, and specific heat cs is fully illuminated by a perpendicular beam of a plane electromagnetic wave.The magnitude of the maximum electric field of the wave is Em.What is the rate dT/dt at which the sheet’s temperature increases due to the absorption of the wave?
In a certain experiment, a radio transmitter emits sinusoidal electromagnetic waves of frequency 110.0 MHz in opposite directions inside a narrow cavity with reflectors at both ends, causing a standingwave pattern to occur. (a) How far apart are the nodal planes of the magnetic field? (b) If the standing-wave pattern is determined to be in its eighth harmonic, how long is the cavity?