Download Electromagnetic Waves

Course:
Date:
Names:__________
__________
__________
Electromagnetic Waves
An electromagnetic wave consists of oscillating electric and magnetic fields traveling at the speed of light. The
wave carries both energy and momentum. The intensity of the wave, which is power per unit area, is given by
1
(1)
I=
E m Bm
2µ 0
An applet that displays the relative orientation of E, B and the direction of propagation of the wave can be
found at this link. Use Firefox, select the applet “Electromagnetic Waves” (the forth from the top), download it
and run it. E and B are perpendicular to each other and perpendicular to the direction of propagation. Their
magnitudes are related by E = cB. Using this relationship, we can also write
2
2
cBm
Em
I=
=
.
2µ 0 c 2µ 0
(2)
1) On the simulation select Ez and By (leave all the others boxes unchecked). Run the animation and use the
cursor to rotate the view.
a) What is the direction of motion of the wave?
b) Set the wavelength to λ = 10. In units where c is set to be = 1 (that means λf = c =1) what is its
frequency?
c) Set the wavelength to λ = 4, run the animation, how does its speed change? Is the wave moving
faster, slower or with same speed?
d) Change the magnitude of Ez, Describe how does the magnitude of By changes
Suppose now that λ = 50.0m, c= 3x108 m/s and the E field vibrates with max amplitude of 22.0 V/m.
1.1 What is its frequency?
1.2 What is the magnitude of the B field when the E field has its max amplitude?
1.3 What is the direction (x,y,z?) of the B field when E is in the negative y-direction?
1.4 What are the wave number k and angular frequency ω?
2) Calculate the speed of light in vacuum using the numerical values of ε0 and μ0
3) Consider blue and red light; find their wavelength, frequency and speed (use your textbook, google…):
λBLUE:_______
fBLUE:_________
speedBLUE:_______
λRED:________
fRED:__________
speedRED:________
4) Calculate the wavelengths and identify which kind of waves are in the EM spectrum
4.1 60 Hz
4.2 93.3 MHz
4.3 4.74 x 1014 Hz
4.4 21 x 1018 Hz
4.5 Which of the above is the fastest EM wave?
5) The intensity of the sunlight incident on the earth’s upper atmosphere is 1340 W/m2.
5.1 What are the peak values of the electric and magnetic fields associated with the sunlight?
Em:____________
Bm:_______________
6) A normal light bulb of a 60 Watts desk lamp has efficiency of 5% (that means that the 95% of the energy
used is wasted into heat). Your sheet of paper is on the desk at a distance d=0.3m below the lamp. Find the max
values of the electric and magnetic fields hitting your piece of paper.
7) From Maxwell’s equations, which terms in these equations represent the sources of the E and B field?
E
B
8) Which of the Maxwell’s equations do prove that light is composed of E and B field?
9) Which one of the Maxwell equations was generalized by Maxwell? And which term did he add?