Chapter 6: Electron Optics

Example 6.1, Page 6.20

In [3]:
from math import sqrt

# Given 
V = 500 # voltage across the electrode in eV
m = 9e-31 # mass of electron in kg
e = 1.6e-19 # charge on an electron in coulomb

#Calculations
E = e * V
v = sqrt((2 * e * V) / m)
p = m * v

#Result
print "Energy gained by electron = %.e J\nSpeed of electron = %.2e meter/sec\nMomentum of electron = %.2e kg-meter/sec"%(E,v,p)

Energy gained by electron = 8e-17 J
Speed of electron = 1.33e+07 meter/sec
Momentum of electron = 1.20e-23 kg-meter/sec

Example 6.2, Page 6.20

In [3]:
# Given 
v = 2.5e6 # speed of electron in meter/sec
B = 2e-4 # magnetic field in tesla
r = 1.76e11 # ratio of charge on electron to the mass of electron in C/kg

#Calculations
a = (B * r * v)

#Result
print "Momentum of acceleration = %.2e meter/square sec."%a

Momentum of acceleration = 8.80e+13 meter/square sec.

Example 6.4, Page 6.21

In [4]:
 
# Given that
v = 5.2e6 # speed of electron in meter/sec
B = 1.3e-4 # magnetic field in tesla
r = 1.76e11 # ratio of charge on electron to the mass of electron in C/kg
E = 3.2e-12 # energy of the electron beam in J
M = 9e-31 # mass of an electron in kg

R = v / (r * B)
v_ = sqrt((2 * E) / M )

print "Radius of circle traced by the beam = %.1f cm. \nSpeed of beam in second case = %.2e meter/sec"%(R*100,v_)
print "Speed of beam in second case is greater than speed of light so we cannot use above formula."

Radius of circle traced by the beam = 22.7 cm. 
Speed of beam in second case = 2.67e+09 meter/sec
Speed of beam in second case is greater than speed of light so we cannot use above formula.

Example 6.5, Page 6.22

In [5]:
# Given 
V = 2.500e3 # voltage across the electrode in V
E = 3.6e4 # strength of electric field in V/m
B = 1.2e-3 # magnetic field in tesla

#Calculation
r = (E / B)**2 / (2 * V)#calculation for ratio of the charge on an electron to the mass of an electron

#Result
print "Ratio of the charge on an electron to the mass of an electron = %.1e C/kg."%r

Ratio of the charge on an electron to the mass of an electron = 1.8e+11 C/kg.

Example 6.6, Page 6.23

In [6]:
from math import sqrt

# Given 
M = 9.1e-31 # mass of electron in kg
E = 1.6e-15 # energy of electron in J
B = 5e-5 # magnetic field in tesla
e = 1.6e-19 # charge on an electron in coulomb

#Calculations
v = sqrt((2 * E) / M)
r = (M * v) / (e * B)

#Result
print "Larmoure radius = %.2f meter"%r

Larmoure radius = 6.75 meter

Example 6.7, Page 6.23

In [7]:
# Given 
Mp = 1.67e-27 # mass of proton in kg
v = 3e5 # speed of proton in meter/sec
B = 5e-9 # magnetic field in tesla
e = 1.6e-19 # charge on a proton in coulomb

#Calculation
r = (Mp * v) / (e * B)#calculation for Larmour radius

#Result
print "Larmour radius = %.2e meter"%r

Larmour radius = 6.26e+05 meter

Example 6.8, Page 6.23

In [8]:
from math import sqrt, pi

# Given 
M = 6.68e-27 # mass of helium ion in kg
E = 1.6e-16 # energy of helium ion in J
B = 5e-2 # magnetic field in tesla
e = 1.6e-19 # charge on helium ion in coulomb

#calculations
v = sqrt((2 * E) / M)#calculation for velocity
r = (M * v) / (e * B)#calculation for Larmour radius
A = pi * r**2#calculation for area traced by the trajectory of helium ion

#Result
print "Area traced by the trajectory of helium ion = %.3f square meter"%A

Area traced by the trajectory of helium ion = 0.105 square meter

Example 6.9, Page 6.23

In [9]:
# Given 
E = 100 # strength of electric field in V/m
B = 1e-3 # magnetic field in tesla

#Calculation
v = E / B

#Result
print "The drift of the guiding center = %.e m/sec"%v

The drift of the guiding center = 1e+05 m/sec

Example 6.10, Page 6.24

In [10]:
# Given 
v = 1e6 # velocity of ion beam in m/sec
B = 1 # magnetic field in tesla

#Calculation
E = B * v

#Result
print "Internal electric field = %.e V/m"%E

Internal electric field = 1e+06 V/m

Example 6.12, Page 6.24

In [11]:
# Given 
r = 1.1 # ratio of new number of turns to the initial number of turns

#Calculation
r_ = (1 / r)**2

#Result
print "Ratio of the new focus length to the initial focus length = %.3f "%r_

Ratio of the new focus length to the initial focus length = 0.826