Question

A plane electromagnetc sinusoidal wave of frequency 40 MHz
tavels free space in the x-direction. at some point and at some
instant, the electric field **E** has its maximum
value of 700 N/C and is along the y-axis. (a.) draw an illustration
of the electromagnetic wve in a coordinate system, and determine
the wavelength and period of the wave. (b.) calculate the magnitude
and direction of the magnetic field B when **E**= 700
N/C in the x-direction. (c) what is the instantaneous energy
density of the wave? (d) write an expression for the equation for
the electric and magnetic field compnents of this electromagnetic
wave.

Answer #1

**given**

**f = 40 Mhz = 40*10^6 Hz
Emax = 700 N/c**

**a)**

**wavelength, lamda = c/f**

**= 3*10^8/(40*10^6)**

**= 7.5 m**

**period, T 1/f**

**= 1/(40*10^6)**

**= 2.5*10^-8 s**

**b) Bmax = Emax/c**

**= 700/(3*10^8)**

**= 2.33*10^-6 T**

**direction of B: towards +z axis**

**c) Energy density = epsilon*Emax^2**

**= 8.854*10^-12*700^2**

**= 4.34*10^-6 J/m^3**

**d) w = 2*pi*f = 2*pi*40*10^6 = 2.51*10^8
rad/s**

**k = 2*pi/lamda = 2*pi/7.5 = 0.838**

**we know,**

**E = Emax*sin(kx - w*t) j**

**= 700*sin(0.838*x - 2.51*10^8*t) j**

**B = Bmax*sin(kx - w*t) k**

A sinusoidal electromagnetic plane wave is traveling in the +y
direction under water, with an index of refraction n = 1.33. The
wave is polarized along the z-axis and has a vacuum wavelength of
A_0 = 500nm.
A. What is the phase velocity of the wavefront in water?
B. What is the wavenumber of the electromagnetic wave in
water?
C. What is the linear frequency of the electromagnetic wave in
water?
D. If the electric field amplitude is 31.0 V/m,...

a plane electromagnetic sinusoidal wave propagating in the x
direction. Suppose the wavelength is 48.0 m and the electric field
vibrates in the xy plane with an amplitude of 20.0 V/m.
(a) Calculate the frequency of the wave.__________ MHz
(b) Calculate the magnetic field B when the electric field has
its maximum value in the negative y direction. magnitude
__________nT
(c) Write an expression for B with the correct unit vector, with
numerical values for Bmax, k, and ω,
and...

Consider a sinusoidal electromagnetic wave propagating in the +x
direction, whose electric field is parallel to the y axis. The wave
has wavelength 475 nm, and the electric field has amplitude 3.20 x
10^-3 V m-1. What is the frequency of the wave? What is the
amplitude of the magnetic field? What are the vector equations for
E(x,t) and B(x,t)?

A sinusoidal plane electromagnetic wave having a frequency of
3.00 GHz travels in the positive x direction. If the amplitude of
the electric field is 300 V.m-1 and the speed of light in vacuum is
taken as 3.0 x 108 m.s-1, write down wave equation in terms of
E(x,t) and B(x,t), where x is in meters and t is in seconds for the
electric field and the magnetic field.

A sinusoidal plane electromagnetic wave propagates in
the space in the + y direction. If the direction and amplitude (9V
/ m) of the electrical component of this wave is i, what is the
magnetic direction and amplitude? Emergency please!!

(a) Write down expressions for the electric and magnetic fields
of a sinusoidal plane electromagnetic wave having a frequency of 3
GHz and traveling in the positive x direction. The amplitude of the
magnetic field is 1 μT. b) Verify that E(x, t) = Ae^(i(kx-wt)) or
B(x, t) = C sinkxsinwt is a solution of the one-dimensional wave
equation; A and C are constants.

The plane monochromatic electromagnetic wave has frequency ?,
polarized in the positive ?-axis
direction moving towards the positive ?-axis direction. The
amplitude of the electric field is ?0, and
the start of time is chosen so that at ? = 0, the electric field
has a value ?0/2 at the origin.
Give answers with only the variables above and speed of light is c
and permittivity ?0.
a. Write the electric field of the wave.
b. Find the associated magnetic...

A plane electromagnetic wave varies sinusoidally at 98.2 MHz as
it travels through vacuum along the positive x direction.
The peak value of the electric field is 2.10 mV/m, and it is
directed along the positive y direction.
(a) Find the wavelength.
m
(b) Find the period.
ns
(c) Find the maximum value of the magnetic field.
pT
(d) Write expressions in SI units for the space and time variations
of the electric field. (x is in meters, and t...

A plane wave of wavelength 100 nm is polarized along z direction
and travelling along -x direction with the electric field amplitude
of 300 V/m (in vacuum). The maximum value of wave is at t=0 and
x=0. Write the wave equation of magnetic field Calculate the
intensity and Poynting vector of electromagnetic wave.

A plane electromagnetic wave, with wavelength 4.0 m, travels in
vacuum in the positive direction of an x axis. The
electric field, of amplitude 270 V/m, oscillates parallel to the
y axis. What are the (a) frequency,
(b) angular frequency, and (c)
angular wave number of the wave? (d) What is the
amplitude of the magnetic field component? (e)
Parallel to which axis does the magnetic field oscillate?
(f) What is the time-averaged rate of energy flow
associated with this...

ADVERTISEMENT

Get Answers For Free

Most questions answered within 1 hours.

ADVERTISEMENT

asked 10 minutes ago

asked 11 minutes ago

asked 19 minutes ago

asked 24 minutes ago

asked 24 minutes ago

asked 24 minutes ago

asked 31 minutes ago

asked 31 minutes ago

asked 1 hour ago

asked 1 hour ago

asked 2 hours ago

asked 2 hours ago