Chapter 24 - Electromagnetic Waves Flashcards
A laser cutter (used for cutting thin sheets of material) emits a beam with electric-field
amplitude Emax= 2.76 x 105 V/m over an area of 2.0 mm2. Find (a) the maximum
magnetic field Bmax (b) the maximum energy density umax and average energy density
uav (c) the intensity I = Sav of the beam, and (d) the average power of the beam
By the way, u represents energy density (in J/m^3)
PART A
Use E = cB and isolate for B to get 9.20 x 10^-4 T
PART B
For max
umax= e0Emax^2
= 0.674
For average
uave = 1/2e0Emax^2
= 0.337
PART C
I = cuav
answer is 1.01x10^8
PART D
P = IA
= 202W
A sinusoidal electromagnetic wave of frequency travels in vacuum in the
+x-direction. The magnetic field is parallel to the +y axis and has amplitude
(a) Find the magnitude of the electric field
b) Write the wave functions using B=Bmaxsin(wt-kx)
Use E = CB
To get 1.74 x 10^5 V/m
PART B
Calculate the angular frequency using w = 2pif
3.83 x 10^15
Calculate the wavenumber using k = 2pi/lambda = 2pif/c = w/c
1.28x10^7
The waves always have opposite signs so
B= Bmaxsin(wt-kx)
E=-Eaxsin(wt-kx)
The electric field of a sinusoidal electromagnetic wave obeys the equation
-(375 V/m)sin[(5.97 x 10^15 rad/s)t + (1.99 x 10^7) rad/m)x]
(a) What are the amplitudes of the
electric and magnetic fields of this wave? (b) What are the frequency, wavelength, and period of the wave?
Emax = 375 V/m
Bmax = Emax/c = 1.25utT
w = 5.98…. so f = w/2pi
k = 1.99 so l = 2pi/k
T = 1/f so 1.05 x10^15
Two sources of sinusoidal electromagnetic waves have average powers of 75 W and 150 W and emit
uniformly in all directions. At the same distance from each source, what is the ratio of the maximum electric
field for the 150 W source to that of the 75 W source?
Emax75^2 = 75W
Emax150
————- = sqrt2
Emax75
The vitreous humor, a transparent, gelatinous fluid that fills most of the eyeball, has an
index of refraction of 1.34. Visible light ranges in wavelength from 400 nm (violet) to 700 nm (red), as
measured in air. This light travels through the vitreous humor and strikes the rods and cones at the surface of
the retina. What are the ranges of (a) the wavelength, (b) the frequency
a) lmedium = lair/n
l min = 400/1.34
l max = 700/1.34
b)
f = c/l
use lambda values for l = 400 and l = 700 ofc
to get
fmin = 4.29 x 10^14
fmax = 7.50 x 10^14
