The electric field of a sinusoidal electromagnetic wave obeys the equation E = - 375 (V/m)sin...
Question:
The electric field of a sinusoidal electromagnetic wave obeys the equation {eq}E = - 375\ (V/m)sin ((5.97 \times 10^{15}\ (rad/s)) t + (1.99 \times 10^7\ (rad/m)) x). {/eq}
a. What is the amplitude of the electric field of this wave?
b. What is the amplitude of the magnetic field of this wave?
c. What is the frequency of the wave?
d. What is the wavelength of the wave?
e. What is the period of the wave?
f. What is the speed of the wave?
Electromagnetic Wave
An electromagnetic wave is a transverse wave and it does not require a medium for its propagation. It is a nonmechanical wave. An electromagnetic wave consists of mutually perpendicular electric field oscillations and magnetic field oscillations. In an electromagnetic wave, the mutually perpendicular electric field oscillations and magnetic field oscillations can be in any direction perpendicular to the direction of propagation. An electromagnetic wave can be represented by a periodic function.
- Electric field and magnetic field oscillations in an electromagnetic wave propagating in the x direction can be represented as {eq}E_y = E_0 \sin ( \omega t - k x ) \\ B_z = B_0 \sin ( \omega t - k x ) {/eq} In this equation {eq}E_0, \ \ B_0, \ \ \omega, \ \ k, \ \ t {/eq} are the electric field amplitude, magnetic field amplitude, angular frequency, wave vector and time respectively.
- In an electromagnetic wave electric field amplitude and magnetic field amplitude are related by the equation {eq}\dfrac { E_0} { B_0} = c {/eq}. Here c is the speed of light in vacuum or the speed with which electromagnetic wave propagate in vacuum.
Answer and Explanation: 1
Become a Study.com member to unlock this answer! Create your account
View this answerGiven data
- The electric field part of the sinusoidal electromagnetic wave {eq}E = - 375 \ \rm { (V/ m ) } \sin ( 5.97 \times 10^{15} \rm { (rad/s) }...
See full answer below.
Ask a question
Our experts can answer your tough homework and study questions.
Ask a question Ask a questionSearch Answers
Learn more about this topic:
Get access to this video and our entire Q&A library
Electromagnetic Waves: Definition, Sources, Properties & Regions
from
Chapter 16 / Lesson 3
20K
Electromagnetic waves are created when there are vibrations between an electric and a magnetic field. This lesson explores electromagnetic waves, looking at the sources, properties and regions in which they exist.
Related to this Question
- The electric field of a sinusoidal electromagnetic wave obeys the equation E = -(400V/m)sin(5.95 x 10^15rad/s)t + (2.00 x 10^7 rad/m)x. A. What is the amplitude of the electric field of this wave? B. What is the amplitude of the magnetic field of this wav
- The electric field of a sinusoidal electromagnetic wave obeys the equation E=-(375V/m)sin[(5.97 \times10^{15}rad/s)t+(1.99 \times10^7rad/m)x] . a. what is the amplitude of the electric field of this w
- The electric field of a sinusoidal electromagnetic wave obeys the equation E = (375 V/m) cos[(1.99 x 10^7 rad/m)x + (5.97 x 10^{15} rad/s)t]. (a) What is the speed of the wave? (b) What is the amplitu
- The electric field of a sinusoidal electromagnetic wave obeys an equation. (A) What is the speed of the wave? (B) What is the amplitude of the electric field of this wave? (C) What is the amplitude of
- If a sinusoidal electromagnetic wave with intensity 10 W/m^{2} has an electric field of amplitude E, then a 20 W/m^{2} wave of the same wavelength will have an electric field of amplitude?
- The electric field of a sinusoidal electromagnetic wave obeys the equation E = (375V /m) cos[(1.99 *10^7rad/m)x + (5.97*10^{15}rad/s)t]. (a) What is the speed of the wave? (b) What are the amplitudes
- Consider a sinusoidal electromagnetic wave propagating in the +x-direction, whose electric field is parallel to the y-axis. The wave has a wavelength of 475 nm, and the electric field has an amplitude of 3.20 times 10^{-3} V m^{-1}. a. What is the frequen
- A traveling sinusoidal electromagnetic wave in vacuum has an electric field amplitude of 68.7 V/m. Find the intensity of this wave and calculate the energy flowing during 13.1 s through an area of 0.0
- A traveling sinusoidal electromagnetic wave in a vacuum has an electric field amplitude of 56.9 V/m. Find the intensity of this wave and calculate the energy flowing during 15.9 s through an area of 0
- A traveling sinusoidal electromagnetic wave in vacuum has an electric field amplitude of 95.1V/m. Find the intensity of this wave and calculate the energy flowing during 12.3s through an area of 0.028
- A plane electromagnetic wave has a frequency of 6.4 \times 10^{14} Hz and an electric field amplitude of 320 N/C. Write equations in the form E(x,t) = E_m cos(kx - \omega t) and B(x,t) = B_m cos(lx -
- 1) The magnetic field of a plane electromagnetic wave is given by B_z = 92.9 sin(kx - 8.73 times 10^6 t) n T. (a) What is the amplitude of the electric field of this wave? 2) An electromagnetic wave i
- The electric field of an electromagnetic wave in a vacuum is E= 20 \frac{V}{m} \sin(6.28 \times 10^8m^{-1}x-\omega t). What is the wave's: a) Wavelength? b) Frequency? c) Magnetic field amplitude?
- The electric field in a radio wave traveling through vacuum has amplitude 2.5 x 10^-4 V/m and frequency 1.47 MHz. a) Find the amplitude and frequency of the magnetic field. b) The wave is traveling in the +x direction. At x = 0 and t = 0, the electric f
- The electric field intensity of a uniform plane wave is given by \vec E = 37.7 \cos (6\pi \times 10^8t + 2\pi z) a_y \ V/m. Find: a) the frequency, b) the wavelength, c) the phase velocity, d) the direction of propagation of the wave, and e) the
- The magnetic field amplitude of an electromagnetic wave is 2.5 \times 10^{-6}\ \rm{T}. The speed of light is 2.99792 \times 10^8\ \rm{m/s}. Calculate the amplitude of the electric field if the wave is traveling in free space.
- An electromagnetic wave in a vacuum has an electric field amplitude of 432 V/m. What is the magnetic field amplitude of this wave? (Answer in T)
- The electric field in a radio wave traveling through vacuum has amplitude 2.9 \times10^{-4} V/m and frequency 1.38 MHz. (a) Find the amplitude and frequency of the magnetic field. (b) The wave is traveling in the +x-direction. At x = 0 and t = 0, the elec
- An electromagnetic wave in a vacuum has an electric field amplitude of 100 V/m and a frequency of 60 kHz. Calculate the a) amplitude, b) frequency of the corresponding magnetic field.
- A travelling wave is propagating in +x direction with an angular frequency of 6.0 \times 10^{12} \; rad/s. Its magnetic field is oscillating along y-direction with an amplitude of 1.2 \times 10^{-6} \; T. Find a) the amplitude for its electric field whe
- An electromagnetic wave in vacuum has an electric field amplitude of 220 volts per meter. What is the amplitude of the corresponding magnetic wave?
- In SI units, the electric field in an electromagnetic wave is described by E_y = 116 sin (1.40 times 10^7x - omega t). (a) Find the amplitude of the corresponding magnetic field oscillations. (b)
- A travelling wave is propagating in +x direction with an angular frequency of 6 \times 10^{12} rad/s. Its magnetic field is oscillating along y-direction with an amplitude of 1.2 \times 10^{-6} \; T. Find: a) the amplitude for its electric field. b) the d
- What is the electric field amplitude of an electromagnetic wave whose magnetic field amplitude is 1.6 mT ?
- What is the electric field amplitude of an electromagnetic wave whose magnetic field amplitude is 1.22 mT?
- What is the electric field amplitude of an electromagnetic wave whose magnetic field amplitude is 2.0 mT?
- What is the electric field amplitude of an electromagnetic wave whose magnetic field amplitude is 1.9 mT?
- The amplitude of the electric field component of an electromagnetic wave is increased from E to 4E. What is the corresponding change in the in the intensity of the wave?
- In a traveling electromagnetic wave, the electric field is represented mathematically as E = E0 sin (1.3E10s^-1t - (7.2E1)x where E0 is the maximum field strength. a) What is the frequency of the wave? b) This wave and the wave that results from its refle
- A sinusoidal electromagnetic wave propagates in a vacuum in the positive x-direction. The B field oscillates in the z-direction. The wavelength of the wave is 30 nm and amplitude of the B field oscill
- The magnetic field of an electromagnetic wave is described by B_y = B_0cos(kx - \omega t), where B_0 = 6.5 \times 10^{-6} T and \omega = 9 \times 10^7 rad/s. (a) What is the amplitude of the corresponding electric field oscillations, E_0, in terms of B_0?
- A harmonic plane wave in a vacuum has an electric field given by: E = Ey sin(kxx minus wt)j minus Ezsin(kxx minus wt)k. Where Ey = 1.8 V/m, Ez = 2.3 V/m, lambda = 1.2mu m. Calculate the amplitude of the wave.
- A sinusoidal electromagnetic wave having a magnetic field of amplitude 1.90 \mu T and a wavelength of 408 nm is traveling in the +x direction through empty space. (a) What is the frequency of this wave? (b) What is the amplitude of the associated electr
- What is the magnetic field amplitude of an electromagnetic wave whose electric field amplitude is 25 V/m?
- What is the magnetic field amplitude of an electromagnetic wave whose electric field amplitude is 10V/m?
- What is the magnetic field amplitude of an electromagnetic wave whose electric field amplitude is 12 V/m?
- If the intensity of the wave at point P is 0.17 W / m^2, what is the electric field amplitude at that point? (c = 3.00 times 10^8 m / s, mu_0 = 4 pi times 10^{-7} T cdot m / A, varepsilon_0 = 8.85
- In a traveling electromagnetic wave, the electric field is represented mathematically as E= E_0\sin [(1.5 \times 10 ^{10} s^{-1}) t - (5.0 \times 10^1 m^{-1}) x] where E_0 is the maximum field strength. a) What is the frequency of the wave? b) This wave
- What is the magnetic field amplitude of an electromagnetic wave whose electric field amplitude is 35 \frac{V}{m}?
- In a traveling electromagnetic wave, the electric field is represented mathematically as E = E0 sin((2.2 x 1010 s-1)t - (6.2 x 101 m-1)x), where E0 is the maximum field strength. (a) What is the frequency of the wave? (b) This wave and the wave that resul
- a) What is the magnetic field amplitude of an electromagnetic wave whose electric field amplitude is 100 V/m? b) What is the intensity of the wave?
- What is the magnetic field amplitude of an electromagnetic wave whose electric field amplitude is 150 V/m? What is the intensity of the wave?
- A plane wave of wavelength 100 nm is polarized along z-direction and traveling along -x-direction with the electric field amplitude of 300 V/m (in vacuum). The maximum value of the wave is at t = 0 and x = 0. a. Write the wave equation of the magnetic fie
- What is the electric field amplitude of an electromagnetic wave whose magnetic field amplitude is 2.22 times 10^{-3} T?
- A plane electromagnetic sinusoidal wave of frequency 44.1 MHz travels in free space. The speed of light is 2 .99792 \times 10^8 \; m/s. (a) Determine the wavelength of the wave. (b) At some point and some instant, the electric field has a value of 662 V/m
- The electric fields received at point P from two identical, coherent wave sources are \vec E_1(t)=E\cos(\omega t+\phi) \hat y and \vec E_2(t)=E\cos (\omega t) \hat y a. Find the resultant wave, b. What is the amplitude of this resultant wave? c. Use the
- The amplitude of the B field of an EM wave is 2.3 x10^-7T . The wave travels in free space A) What is the amplitude of the E field? B) What is the average power per unit area of the EM wave?
- In SI units, the electric field in an electromagnetic wave is described by: E_y = 106 sin(1.40 x 10^ 7 x - omega t) (a) Find the amplitude (in mu T) of the corresponding magnetic field oscillations. (b) Find the wavelength lambda (in mu m). (c) Find the f
- In a traveling electromagnetic wave, the electric field is represented mathematically as E = E_0 sin[(1,44 \times 10^10s^{-1} )t- (48 m^{-1}) x] where E_0 is the maximum field strength. (a) What is the frequency of the wave?
- A plane electromagnetic wave, with a wavelength of 3.8 m, travels in vacuum in the positive direction of an x-axis. The electric field, of amplitude 340 V/m, oscillates parallel to the y-axis. a. What are the frequency, angular frequency, and angular wave
- The electric field phasor of a uniform plane wave is given by \tilde{E} = \hat{y}10e^{-j0.2z}(V/m) If the phase velocity of the wave is 1.5 * 108 m/s and the relative permeability of the medium is μr = 2.4 find the following: a) The wavelength b) Th
- The amplitude of the B field of an EM wave is 2.2 x 10-7 T. The wave travels in free space. What is the amplitude of the E field? What is the average power per unit area of the EM wave?
- In an EM wave traveling west, the B-field oscillates vertically and has a frequency of 50.0 kHz and an rms strength of 6.75 \times 10^{-9} T. \\ A. What is the frequency of the electric field? B. What is the rms strength of the electric field?
- A plain electromagnetic wave traveling in vacuum is measured to have intensity I = 0.2 W/m^2. The dielectric permittivity of vacuum is 8.854 x 10^( 12) F/m. Find the amplitude of the magnetic field Bm in the wave.
- An EM wave has an electric field with an rms value of 7.3 times 10^7 V/m and a wavelength of 285 nm. (a) What is the frequency of the electric field? (b) What is the value of the magnetic field? (c) What is the frequency of the magnetic field?
- In an EM wave travelling west, the B field oscillates vertically and has a frequency of 78.0 kHz and an rms strength of 6.00 \times 10^{-9} \; T. What is the frequency of the electric field? What is the rms strength of the electric field?
- The electric field of an electromagnetic wave in a vacuum is E_y = (16.0 V/m) cos((2.78 x 10^8)x - omega t), where x is in m and t is in s. (A) What is the wave's wavelength? (B) What is the wave's fr
- A plane electromagnetic wave, with wavelength 2.0 m, travels in a vacuum in the positive direction of an x axis. The electric field, of amplitude 150 V/m oscillates parallel to the y axis. What are the (a) frequency, (b) angular frequency, and (c) angular
- A plane electromagnetic wave, with wavelength 3.8 m, travels in vacuum in the positive direction of an x axis. The electric field, of amplitude 240 V/m, oscillates parallel to the y axis. What are the (a) frequency, (b) angular frequency, and (c) angular
- If the intensity of an electromagnetic wave is 80 MW/m2, what is the amplitude of the magnetic field of this wave?
- The magnetic field of an electromagnetic wave in a vacuum has the following equation, where x is in meters and t is in seconds: B = (3.0 micro T) sin (1.0 \times 10^7 x - 2 \pi f t)z. What is the wave
- The magnetic field of an electromagnetic wave in a vacuum is B_z = (2.4\ T) sin((1.14 \times 10^7) x - \omega t), where x is in meters and t is in s. (a) What is the wave's wavelength? (b) What is the wave's frequency? (c) What is the wave's electric
- A sinusodial electromagnetic wave has an electric field whose rms value is 100 V/m. What is the instantaneous rate S of energy flow for this wave?
- The magnetic field of an electromagnetic wave in a vacuum is B = (2.5 muT) sin ((1.5 x 10^7)x - 2pift), where x is in m and t is in s. a. What is the wave's wavelength? b. What is the wave's frequency
- A plain electromagnetic wave traveling in vacuum is measured to have intensity I = 0.2 W/m2. The dielectric permittivity of vacuum is Eo= 8.854x10^-12 F/m. Find the amplitude of the magnetic field Bm in the wave.
- Three sinusoidal waves of the same frequency travel along a string in the positive direction of an x axis.Their amplitudes are y1, y1/2, and y1/4, and their phase constants are 0, π/2, and π,respectively. (a) What is the amplitude of the resultant
- A standing wave on a string with a length of 14.3\ \mathrm{m} has 8 antinodes and is generated by a 120\ \mathrm{Hz} oscillator. The amplitude is 22\ \mathrm{mm}. Write the equation for this standing wave.
- A sinusoidal wave of amplitude 3 m travels with a frequency of 10 Hz on a string of linear mass density 0.2 kg m^{-1}, length 10 m and tension 10 N. (a) Write an expression for the wave's transverse d
- 1. The magnetic field of an electromagnetic wave is given by B(x,t)=(0.3u T)sin[(10pi x10^6m^-1 )x-(30pi x10^15 s^-1 )t]. Find the amplitude of the electric field. 2. Which of the following requires
- The magnetic field of an electromagnetic wave in a vacuum is B_z = (3.0 \mu T)\sin((1.0 \times 10^7)x - \omega t) , where x is in m and t is in seconds. What is the wave's wavelength? What is the wave's frequency? What is the wave's electric field amplitu
- The electric field of an electromagnetic wave in a vacuum is E_y = (17V/m) sin((2.78x10^8 )x-wt), where x is in am and t is in s. What is the wave's magnetic field amplitude?
- The electric field of an electromagnetic wave traveling in a medium with epsilon_r = X is described by the wave function of vector E (x, y) = (9 times 10^5 V/m) hat Y cos (k x - (Z s^-1) t) (a) In which direction is the wave traveling? (b) What is the wav
- A 550 nm harmonic EM-wave whose electric field is in the z-direction is traveling in the y-direction in vacuum. (a) What is the frequency? (b) Determine both w and k for this wave. (c) If the field's
- A transverse traveling wave on a taut wire has an amplitude of 0.200 mm and a frequency of 600 Hz. It travels with a speed of 196 m/s. (a) If the wave equation is written in the form y = A sin(kx - om
- A transverse traveling wave on a taut wire has an amplitude of 0.200 mm and had a frequency of 550 Hz. It travels with a speed of 196 m/s. a) If the wave equation is written in the form y = A sin(kx
- A plane electromagnetic sinusoidal wave of frequency 40 MHz travels in free space in the x-direction. At some point and at some instant, the electric field E has its maximum value of 750 V/m and is al
- Write the wave equation for the electric field of an electromagnetic wave that is traveling in the +z direction with a wavelength of 2.0 m and an amplitude of 100 N/C. Give the equation of its angular
- The electric field in a microwave traveling through air has amplitude 0.61 mV/m and frequency 37 GHz. Find the amplitude and frequency of the magnetic field. (Give your answer in scientific notation.
- Electromagnetic wave 1 has a maximum electric field of E_0 = 52 V/m, and electromagnetic wave 2 has a maximum magnetic field of B_0 = 1.5 \mu T. a) Calculate the intensity of each wave. b) Which wave
- The electric field of a plane wave propagating in a vacuum is given by: E = E0e^i (kx- omega t) j, where E0 = 98 V/m, k = 1.4 x 10^7 rad/m, and omega = 2.8 x 10^15 rad/s. What is the irradiance of this wave?
- An electromagnetic wave of wavelength 235 nm is traveling in vacuum in the z-direction. The electric field has an amplitude 2.70 x 10^{-3} V/m and is parallel to the x-axis What is the frequency of th
- An electromagnetic wave of wavelength 435 nm / s tgraveling in vaccum in the z-direction. The electric field has an amplitude of 2.79 x 10^-3 V/m and is parallel to the x axis. What are the frequency
- The magnetic field associated with an electromagnetic wave has an amplitude of 1.7 mu*T. (a) What is the amplitude of the electric field associated with this wave? (b) What is the intensity of this wave? (c) What is the radiation pressure associated with
- The magnetic field of an electromagnetic wave is given by B(x, t) = (0.8 \mu T) sin[(8.00\pi \times 10^6 m^{-1})x - (2.40 \pi \times 1015 s^{-1})t]. Calculate the following. (a) the amplitude of the
- In a traveling electromagnetic wave, the electric field is given by E = E0 sin((6.28 x 109 rad/s)t - (20.9 m-1)x) where E0 is the maximum field strength. What is the wavelength of the wave? (a) 100 m (b) 30 m (c) 2 m (d) 0.3 m (e) 0.048 m
- A sinusoidal electromagnetic wave emitted by a cellular phone has a wavelength of 34.5 cm and an electric-field amplitude of 6.20 x 10^{-2} V/m at a distance of 350 m from the antenna. a) Calculate th
- The following equation can be given for a transverse wave traveling on a string, y = A sin (k x - w t). A = 2 mm, k = 19 rad/m, w = 480 rad/sec (a) Find the amplitude of the transverse wave. (b) Find the frequency. (c) Find wave velocity. (d) Give the wav
- An EM wave's electric field oscillates with E_y = Esin (2pi (x/lambda-ft)), where E_0 = 5.000 times 10^5 N/C, and lambda = 8.000 times 10^{-7} m (infrared light). (a) Calculate f, the wave's linear frequency. (b) Calculate the magnitude of the magnetic fi
- A sinusoidal plane electromagnetic wave travels in a vacuum in the x direction. The period of the wave, T, is 9.8 x 10^-8 s. (a) Express the wavelength of the wave, λ, in terms of T and the sp
- A laser beam with wavelength 633 nm is propagating in the z-direction. Its electric field is parallel to the x axis and has amplitude 6.0 kV/m. Find the wave frequency, the direction and amplitude of the magnetic field.
- A laser beam with wavelength 633 nm is propagating in the z-direction. Its electric field is parallel to the x axis and has an amplitude of 6.0 kV/m. Find the wave frequency, the direction and amplitude of the magnetic field.
- 1. A string under the tension of 200 N oscillates at a fundamental frequency of 420 Hz. At what tension would it oscillate at 440 Hz? 2. Two charges +4 nC and -1 nC are separated by 16 mm. Find the point where the net electric field is zero?
- The amplitude of a wave is 0.2 m. The time period of the vibration is 0.5 secs. Calculate the frequency, velocity and the wavelength of the wave.
- A sinusoidal electromagnetic wave emitted by a cellular phone has a wavelength of 35.4 cm and an electric-field amplitude of 6.00 x 10^-2 V/m at a distance of 210 m from the antenna. Calculate the fre
- A sinusoidal wave emitted by a cellular phone has a wavelength of 36.7 cm and an electric-field amplitude of 5.2 x 10^-2 V/m at a distance of 255 m from the antenna. a) Calculate the frequency of the
- 1. The E field in an EM wave in free space has a peak of 24.3 mV/m. What is the average rate at which this wave carries energy across unit area per unit time? (answer in W/m^2) 2. The amplitude of the
- A sinusoidal electromagnetic wave, emitted by a cellular phone, has a wavelength of 35.9cm, and an electric-field amplitude of 4.90x10^-2V/m, at a distance of 250m from the antenna. Calculate the freq
- A wave traveling in the +x direction has an amplitude of 0.258 m, a speed of 6.87 m/s, and a frequency of 19.7 Hz. Write the equation of the wave.
- An electromagnetic wave has a maximum intensity of 88 W/m^2. What is the peak magnitude of the electric field of this wave?
Explore our homework questions and answers library
Browse
by subject