Download PHYS 222 Worksheet 26 Electromagnetic

PHYS 222
Worksheet 26 – Electromagnetic Waves
Supplemental Instruction
Iowa State University
Leader:
Course:
Instructor:
Date:
Alek Jerauld
PHYS 222
Dr. Paula Herrera-Siklódy
4/2/12
Useful Equations
v
1
 0 0
 c  3108 m / s
E  Emax cos  kx  t  ˆj
B  Bmax cos  kx  t  kˆ
k
2

Speed of light
Harmonic EM wave propagating in x-direction. E and B
are ALWAYS in phase
,   2 f , c   f
E B
Propagation direction
E  cB
Magnitude relationship between E and B fields
v
1


c
 m

c
n
EM wave speed in non-vacuum medium. n is the
refraction index
Diagram:
Related Problems
1) A sinusoidal electromagnetic wave having a magnetic field of amplitude 1.25 µT and a
wavelength of 432 nm is traveling in the +x direction through empty space. (Book 32.5)
(a) What is the frequency of this wave?
c
f   6.94(1014 ) Hz

(b) What is the amplitude of the associated electric field?
E  cB  375 V / m
(c) Write equations for electric and magnetic fields as a function of x and t
Bmax  1.25 T
Emax  375 V / m
  2 f  5.91(1015 ) rad / s
  432(109 ) m
 2

E  Emax cos 
x  t  ˆj
 

 2

B  Bmax cos 
x  t  kˆ
 

2) The electric field of a sinusoidal electromagnetic wave obeys the equation:
. (Book 32.8)
(a) What is the amplitude of the electric field of this wave?
Emax  375 V / m
(b) What is the amplitude of the magnetic field of this wave?
Bmax  1.25 T
(c) What is the frequency of the wave?

f 
 9.50(1014 ) Hz
2
(d) What is the wavelength of the wave?
2

 316 nm
k
(e) What is the period of the wave?
1
T   1.05(1015 ) s
f
(f) Is this light visible to humans?
No, humans can see within the wavelength range of 390 to 750 nm.
(g) What is the speed of the wave?
v   f  3(108 ) m / s
3) An electromagnetic wave with frequency 64.0 Hz travels in an insulating magnetic
material that has dielectric constant 3.64 and relative permeability 5.18 at this frequency.
The electric field has amplitude 7.20(10-3) V/m. (Book 32.14)
(a) What is the speed of propagation of the wave?
c
v
 9.91(107 ) m / s
 m
(b) What is the wavelength of the wave?
v
   1.06(106 ) m
f
(c) What is the amplitude of the magnetic field?
E
E
B 
 1.04(106 ) T
c f