Introduction To Special Relativity And Space Science (By S.P. Singh)

CHAPTER NUMBER 2 : ELECTROMAGNETIC WAVES

EXAMPLE NUMBER 2.3 : (Page Number 80)

In [20]:
import math
# Given That
I = 2.4 # intensity of radiation in Watt per meter square
epsilon1_0 = 8.85e-12
c = 3e8
E = sqrt ((2* I)/ (c * epsilon1_0)) # calculation of amplitude of electric field is
print "Amplitude of electric field is ",round(E,4)," N/C  "
Amplitude of electric field is  42.5195  N/C  

EXAMPLE NUMBER 2.4 : (Page Number 80)

In [22]:
import math
# Given That
l = 75 # length of laser beam in cm
power = 6e-3 # power of beam in mW
c = 3e8
t = l / ( c * 100) #calculation of time taken to cover distance
U =  power/1000 * t#calculation of Energy stored in given length
print "Energy stored in given length is ",U," J  "
Energy stored in given length is  1.5e-14  J  

EXAMPLE NUMBER 2.6 : (Page Number 81)

In [26]:
import math
# Given That
E_0 = 300 # maximum electric field in electromagnetic wave in w/m
v = 2e8 # speed of moving electron in m/s along y - axis
c = 3e8 # speed of light in m/s
q = 1.6e-19 # charge on electron in coulomb
B_0  = E_0 / c # calculation of magnitude of maximum magnetic field
F_e = q*E_0 # calculation of electromagnetic force on electron in N
F_b = q*v*B_0 # calculation of magnetic force on electron in N
print "The maximum electric force on electron is  ",F_e," N along y -axis  "
print "The maximum magnetic force on electron is  ",F_b," N along z - axis "
The maximum electric force on electron is   4.8e-17  N along y -axis  
The maximum magnetic force on electron is   3.2e-17  N along z - axis 

EXAMPLE NUMBER 2.7 : (Page Number 82)

In [30]:
import math
# Given That
d = 1.5e11 # separation between earth and sun in meter
power_sun = 3.8e26# power radiated by sun in W
c = 3e8
s = power_sun /(4 * pi * (d**2)) #calculation of Energy received per unit surface area per unit time
p =  s / c # calculation of Pressure applied by sun radiations on earth
print "Energy received per unit surface area per unit time is ",s,""
print "  Pressure applied by sun radiations on earth is ",p," N/m**2  "
Energy received per unit surface area per unit time is  1343.975075 
  Pressure applied by sun radiations on earth is  4.47991691666e-06  N/m**2  

EXAMPLE NUMBER 2.8 : (Page Number 83)

In [31]:
import math
# Given That
E = 100 # magnitude of electric field perpendicular to X axis in N/C
r = 10 # radius of circle in cm
ds = (r*1e-2)**2 #calculation of area of coil
phi1 = E*ds #calculation of Flux through coil
print "Flux through coil is  ",phi1," Nm/C  "
Flux through coil is   1.0  Nm/C  

EXAMPLE NUMBER 2.9 : (Page Number 84)

In [33]:
import math
# Given That
sigma1 = 2e-6 # surface charge density in c/m**2 on XY plane
theta1 = 60 # angle between normal and X axis on degree
r = 10 # radius of circle in cm
epsilon1_0 = 8.85e-12 # permitivity of free space
print "standard formula used   phi1 = sigma1*A*cos(theta1)/(2*epsilon1_0)   "
phi1 = sigma1* pi*(r*1e-2)**2 * cos (theta1*pi/180) / (2*epsilon1_0) #calculation of Flux through coil
print "Flux through coil is  ",round(phi1,4)," Nm**2/C.  "
standard formula used   phi1 = sigma1*A*cos(theta1)/(2*epsilon1_0)   
Flux through coil is   1774.9111  Nm**2/C.  

EXAMPLE NUMBER 2.10 : (Page Number 84)

In [35]:
import math
# Given That
A = 200 # magnitude of electric field in V/m**2
epsilon1_0 = 8.85e-12 # permittivity of free space
a = 20 # radius of sphere in cm
q = 4*pi * epsilon1_0*A*(a*1e-2)**3  #calculation of Charge contained in sphere
print "Charge contained in sphere is  ",q," C.  "
Charge contained in sphere is   1.77939807899e-10  C.  

EXAMPLE NUMBER 2.11 : (Page Number 84)

In [37]:
import math
# Given That
B = 0.2 #  magnetic field in T
del_r = 1 # rate of change of decrement in loop radius in cm/s
r =  20 # radius of frame in cm
R = 10 # resistance of frame in m ohm
e =  2* pi * B *r *1e-2* del_r*1e-2 # magnitude of emf induced in coil
i = (e) / (R*1e-3) #calculation of Current induced due to changing magnetic field
print "Current induced due to changing magnetic field is ",round(i,4)," A  " 
Current induced due to changing magnetic field is  0.2513  A  

EXAMPLE NUMBER 2.12 : (Page Number 85)

In [40]:
import math
# Given That
phi1 = 0.02 # rate of change of magnetic field in T/s
r =  2 # radius of frame in cm
R = 2 # resistance of frame in m ohm
a = pi * (r*1e-2)**2
e =  a * phi1 # magnitude of emf  induced in coil
i = (e) / (R*1e-3) 
print "Current induced due to changing magnetic field is ",round(i*1000,4)," mA  " 
Current induced due to changing magnetic field is  12.5664  mA  

EXAMPLE NUMBER 2.13 : (Page Number 86)

In [41]:
import math
# Given That
r = 7e8 # radius sun in meter
power_sun = 3.8e26# power radiated by sun in W
s = power_sun /(4 * pi * (r**2)) #calculation of Pressure applied by sun radiations on earth
print "Pressure applied by sun radiations on earth is ",s," W/m**2  "
Pressure applied by sun radiations on earth is  61713141.1989  W/m**2  

EXAMPLE NUMBER 2.14 : (Page Number 86)

In [43]:
import math
# Given That
solar_const = 2 # energy received by earth from sun in Cal/min cm2
mu_not = 1.2566e-6 # universal constant
epsilon1_not = 8.85e-12 # universal constant
ratio = sqrt(mu_not / epsilon1_not) # constant
E = sqrt (ratio *4.2 * solar_const / 6e-3) 
E_not = E * sqrt(2) #calculation of Amplitude of electric  vectors
H_not = E_not / ratio#calculation of Amplitude of magnetic vectors
print "Amplitude of electrical and magnetic vectors are given as ",round(E_not,4)," V/m and ",round(H_not,4)," A/m"
Amplitude of electrical and magnetic vectors are given as  1027.1703  V/m and  2.7259  A/m

EXAMPLE NUMBER 2.15 : (Page Number 87)

In [45]:
import math
# Given That
r = 1 # distance from lamp in meter
power = 100# power radiated by lamp in W
mu_not = 1.2566e-6 # universal constant
epsilon1_not = 8.85e-12 # universal constant
s = power /(4 * pi * (r**2)) #calculation of intensity at a distance
ratio = sqrt(mu_not / epsilon1_not) #calculation of a constant
E = sqrt (ratio * s) #calculation of Average value of intensity of electric field
print "Average value of intensity of electric field is ",round(E,4)," V/m  "
Average value of intensity of electric field is  54.7594  V/m