Question

In free space, the electric field intensity ? = 20 cos (ωt-50x) ?̂ V/m. ?̂ is the unit vector along y-axis.

Calculate

(i) Displacement current density (?? ?? ).

(ii) Magnetic Field intensity (?)

(iii) Angular frequency (ω).

Assume ? 0 = 4? × 10( −7) and ? 0 = 8.854 × 10 (−12) ?/?

Answer #1

If ?⃗⃗ = 5 cos (?? + ??)?̂ V/m is given in free space and the
time period is 50 ns,
(a) show that this electric field can exit (find the
condition),
(b) determine the magnetic field intensity, and
(c) the direction of power flow.

The electric field of an electromagnetic wave in a vacuum is
Ey=(18.0 V/m)cos((4.18 ×10^8)x−ωt), where x is in m and t is in
s.
What is the wavelength, frequency, and magnetic field amplitude
of the wave?

If the electric field in a plane electromagnetic wave is along
the y axis and its component is given
by Em sin(kx + ωt), in SI units, then the magnetic field is along
the z axis and its component
is given by:
A. (Em/c) cos(kx + ωt)
B. −(Em/c) cos(kx + ωt)
C. −(Em/c) sin(kx + ωt)
D. Em cos(kx + ωt)
E. (Em/c) sin(kx + ωt)
how and why b is wrong

For a particular polarization of light, the time dependent
portion of the electric field Eₒ and
magnetic field Hₒ are given by the
expressions
Eₒ = 4sin(ωt)(i hat) + 4cos(ωt)(j hat)
+ 0(k hat)
Hₒ = 4cos(ωt)(i hat) + 4sin(ωt)(j hat)
+ 0(k hat)
where ω is a constant (the frequency of the light) and t is
time.
a) Show that each field satisfies the wave equation in free
space. (Hint: Don’t forget to include the space-dependent portion
as well.)...

The electric component of a beam of polarized light is
Ey = (5.27 V/m) sin[(1.03 × 106
m-1)z + ωt].
(a) Write an expression for the magnetic field
component of the wave, including a value for ω. What are
the (b)wavelength, (c) period,
and (d) intensity of this light?
(e) Parallel to which axis does the magnetic field
oscillate? (f)In which region of the
electromagnetic spectrum is this wave?

The electric component of a beam of polarized light is Ey =
(5.31 V/m) sin[(1.29 × 106 m-1)z + ωt]. (a) Write an expression for
the magnetic field component of the wave, including a value for ω.
What are the (b) wavelength, (c) period, and (d) intensity of this
light? (e) Parallel to which axis does the magnetic field
oscillate? (f) In which region of the electromagnetic spectrum is
this wave?

1. State Maxwell’s equation for the curl of the magnetic and the
electric field in free space. State the meaning of all the terms in
the equations and identify the displacement current density.

(c ≈ 3.00 x 108 m/s;
εo ≈ 8.85 x 10–12
N-m2/C2; μo = 4π x
10–7 T-m/A)
(a) A plane electromagnetic wave of wavelength 2.00 m travels in
vacuum in the negative x-direction with its magnetic field
vector B, of amplitude 1.20 μT, directed along the
positive y-axis.
(i) What is the frequency, f, of the wave?
[2]
(ii) What are the direction and the amplitude,
Eo, of the electric field vector
E associated with the wave...

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...

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...

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