1) The electric field component of an electromagnetic planar wave is defined by the following equation E(x,t) = (2.6 x 104 N/C)sin[(1.89 x 10\' rad/m)x + (4.96 x 1015 rad/s)j a What are the wavelength and frequency (in hertz) of this wave? b) I the space below, write a vector expression for the magnetic field component of this wave: B( ) What is the intensity of this wave? d) Sinusoidal light described above shines uniformly upon the bottom of a totally absorbing cylinder as shown. The height H of the cylinder is 2.5mm. If the cylinder is suspended in mid-air by the light, what is the density, p, of the cylinder? (hint: gravity pulls down, light pushes up...you don\'t need the area of the cylinder\'s end caps to solve this) What would be the density, p, if the surface of the cylinder was totally reflective?
Solution
(A) E = Em sin[ kx + w t]
k = 2 pi/ wavelength
wavelength = 2 pi / (1.89 x 10^7) = 3.32 x 10^-7 m ....Ans
w = 2 pi f
f = (4.96 x 10^15)/2pi = 7.89 x 10^14 Hz ....Ans
(B) v = wavelength * f= 2.62 x 10^8 m/s
Bm = Em / v = 9.93 x 10^-5 T
B = (9.93 x 10^-5 T) sin[(1.89 x 10^7)x + (4.96 x 10^15)t](-k)
(C) I = Em Bm / (2 u0)
u0 = 4pi x 10^-7
I = 2.05 x 10^6 W/m^2
(D) F = I A / c
as it is suspended, F = m g
I A / v = ( A h rho) g
rho = I / (v h g)
rho = (2.05 x 10^6) / (2.62 x10^8 x 2.5 x 10^-3 x 9.8)
rho = 0.32 kg / m^3 ....Ans
(E) now F = 2 I A / c
rho\' = 2 rho = 0.63 kg / m^3 .....Ans
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1) The electric field component of an electromagnetic planar wave is d.docx
1. 1) The electric field component of an electromagnetic planar wave is defined by the following
equation E(x,t) = (2.6 x 104 N/C)sin[(1.89 x 10' rad/m)x + (4.96 x 1015 rad/s)j a What are the
wavelength and frequency (in hertz) of this wave? b) I the space below, write a vector expression
for the magnetic field component of this wave: B( ) What is the intensity of this wave? d)
Sinusoidal light described above shines uniformly upon the bottom of a totally absorbing
cylinder as shown. The height H of the cylinder is 2.5mm. If the cylinder is suspended in mid-air
by the light, what is the density, p, of the cylinder? (hint: gravity pulls down, light pushes
up...you don't need the area of the cylinder's end caps to solve this) What would be the density,
p, if the surface of the cylinder was totally reflective?
Solution
(A) E = Em sin[ kx + w t]
k = 2 pi/ wavelength
wavelength = 2 pi / (1.89 x 10^7) = 3.32 x 10^-7 m ....Ans
w = 2 pi f
f = (4.96 x 10^15)/2pi = 7.89 x 10^14 Hz ....Ans
(B) v = wavelength * f= 2.62 x 10^8 m/s
Bm = Em / v = 9.93 x 10^-5 T
B = (9.93 x 10^-5 T) sin[(1.89 x 10^7)x + (4.96 x 10^15)t](-k)
(C) I = Em Bm / (2 u0)
u0 = 4pi x 10^-7
I = 2.05 x 10^6 W/m^2
2. (D) F = I A / c
as it is suspended, F = m g
I A / v = ( A h rho) g
rho = I / (v h g)
rho = (2.05 x 10^6) / (2.62 x10^8 x 2.5 x 10^-3 x 9.8)
rho = 0.32 kg / m^3 ....Ans
(E) now F = 2 I A / c
rho' = 2 rho = 0.63 kg / m^3 .....Ans
![1) The electric field component of an electromagnetic planar wave is defined by the following
equation E(x,t) = (2.6 x 104 N/C)sin[(1.89 x 10' rad/m)x + (4.96 x 1015 rad/s)j a What are the
wavelength and frequency (in hertz) of this wave? b) I the space below, write a vector expression
for the magnetic field component of this wave: B( ) What is the intensity of this wave? d)
Sinusoidal light described above shines uniformly upon the bottom of a totally absorbing
cylinder as shown. The height H of the cylinder is 2.5mm. If the cylinder is suspended in mid-air
by the light, what is the density, p, of the cylinder? (hint: gravity pulls down, light pushes
up...you don't need the area of the cylinder's end caps to solve this) What would be the density,
p, if the surface of the cylinder was totally reflective?
Solution
(A) E = Em sin[ kx + w t]
k = 2 pi/ wavelength
wavelength = 2 pi / (1.89 x 10^7) = 3.32 x 10^-7 m ....Ans
w = 2 pi f
f = (4.96 x 10^15)/2pi = 7.89 x 10^14 Hz ....Ans
(B) v = wavelength * f= 2.62 x 10^8 m/s
Bm = Em / v = 9.93 x 10^-5 T
B = (9.93 x 10^-5 T) sin[(1.89 x 10^7)x + (4.96 x 10^15)t](-k)
(C) I = Em Bm / (2 u0)
u0 = 4pi x 10^-7
I = 2.05 x 10^6 W/m^2](https://image.slidesharecdn.com/1theelectricfieldcomponentofanelectromagneticplanarwaveisd-230131003412-0074465a/85/1-The-electric-field-component-of-an-electromagnetic-planar-wave-is-d-docx-1-320.jpg)
