7: Motion of a charged particle

Example number 7.1, Page number 132

In [5]:
#importing modules
import math
from __future__ import division

#Variable declaration
e=1.6*10**-19;                   #charge of the electron(c)
V=18;                            #potential difference(kV)
m=9.1*10**-31;                   #mass of the electron(kg)

#Calculation                        
K=e*V*10**3;                     #Kinetic energy(J)
v=math.sqrt((2*e*V*10**3)/m);            #speed of electron(m/s)

#Result
print "The kinetic energy of electron is",K*10**16,"*10**-16 J"
print "Speed of the electron is",round(v/10**7,3),"*10**7 m/s"
The kinetic energy of electron is 28.8 *10**-16 J
Speed of the electron is 7.956 *10**7 m/s

Example number 7.2, Page number 133

In [7]:
#importing modules
import math
from __future__ import division

#Variable declaration
m=9.1*10**-31;                    #mass of electron(kg)
vx=4*10**6;                       #velocity along x-axis(m/s)
E=1500;                           #electric field strength(N/C)
l=0.07;                           #length in y-axis(m)
q=1.6*10**-19;                    #charge of electron(c)

#Calculation                        
y=(-q*E*(l**2))/(2*m*(vx**2))*10**2;         #vertical displacement of electron(cm)

#Result
print "The vertical displacement of electron when it leaves the electric field is",round(y,3),"cm"
The vertical displacement of electron when it leaves the electric field is -4.038 cm

Example number 7.3, Page number 133

In [9]:
#importing modules
import math
from __future__ import division

#Variable declaration
u=5*10**5;                   #velocity(m/s)
m=1.67*10**-27;               #mass of proton(kg)
q=1.6*10**-19;
E=500;                        #electric field(N/C)
theta=42;                     #angle(degrees)

#Calculation                        
theta=theta*math.pi/180;      #angle(radian)
t=((u*m*math.sin(theta))/(q*E))*10**6;             #time required for the proton(micro s)

#Result
print "The time required for the proton is",round(t,2),"micro s"
The time required for the proton is 6.98 micro s

Example number 7.4, Page number 133

In [12]:
#importing modules
import math
from __future__ import division

#Variable declaration
m=1.67*10**-27;                  #mass of proton(kg)
q=1.6*10**-19;
B=0.36;                          #magnetic field(T)
R=0.2;                           #radius(m)

#Calculation                        
v=(q*B*R)/m;            #orbital speed of proton(m/s)

#Result
print "The orbital speed of proton is",round(v/10**6,1),"*10**6 m/s"
The orbital speed of proton is 6.9 *10**6 m/s

Example number 7.5, Page number 133

In [14]:
#importing modules
import math
from __future__ import division

#Variable declaration
v=2*10**6;                     #speed(m/s)
theta=30;                      #angle at which proton enters at the origin of coordinate system(degrees)
B=0.3;                         #magnetic field(T)
m=1.67*10**-27;                #mass of proton(kg)
q=1.6*10**-19;

#Calculation                        
theta=theta*math.pi/180;       #angle(radian)
vp=v*math.sin(theta);          #v(perpendicular component)
vpa=v*math.cos(theta);         #v(parallel component)
p=(vpa*2*math.pi*m)/(q*B);         #pitch of the helix described by the proton
R=((m*vp)/(q*B))*10**2;         #radius of the trajectory

#Result
print "the pitch of the helix is",round(p,2),"m"
print "the radius of trajectory is",round(R,2),"cm"
the pitch of the helix is 0.38 m
the radius of trajectory is 3.48 cm

Example number 7.6, Page number 133

In [18]:
#importing modules
import math
from __future__ import division

#Variable declaration
V=25;                      #deflecting voltage(V)
l=0.03;                    #length of deflecting planes(m)
d=0.75;                    #distance between 2 deflecting plates(cm)
Va=800;                    #final anode voltage(V)
D=0.2;                     #distance between the screen and the plates(m)
e=1.6*10**-19;
m=9.1*10**-31;                               #mass of electron(kg)

#Calculation                        
y=(((V*l)/(2*d*Va))*(D+(l/2)))*10**4;        #displacement produced(cm)
a=((V*l)/(2*d*Va))*10**2;
alpha=math.atan(a);                          #angle made by the beam with the axis(radian)
alpha1=alpha*180/math.pi;        #angle(degrees)
v=((math.sqrt((2*e*Va)/m))/math.cos(alpha));          #velocity of electron(v)

#Result
print "the displacement produced is",round(y,2),"cm"
print "the angle made by the beam with the axis is",round(alpha1,2),"degrees"
print "velocity of electrons is",round(v/10**7,2),"*10**7 m/s"
the displacement produced is 1.34 cm
the angle made by the beam with the axis is 3.58 degrees
velocity of electrons is 1.68 *10**7 m/s

Example number 7.7, Page number 134

In [20]:
#importing modules
import math
from __future__ import division

#Variable declaration
e=1.6*10**-19;
B=5*10**-5;                  #magnetic field(Wb/m**2)
l=0.04;                      #length of magnetic field along the axis(m)
m=9.1*10**-31;               #mass of electron(kg)
D=0.25;                      #distance of the screen from the field(m)
Va=600;                      #final anode voltage(V)

#Calculation                        
y=(((e*B*l)/m)*math.sqrt(m/(2*e*Va))*(D+(l/2)))*10**2;      #displacement of the electron(cm)

#Result
print "the displacement of the electron beam spot on the screen is",round(y,2),"cm"
the displacement of the electron beam spot on the screen is 0.65 cm

Example number 7.8, Page number 134

In [22]:
#importing modules
import math
from __future__ import division

#Variable declaration
E=2.5*10**4;               #electric field(V/m)
B=0.18;                    #magnetic field(T)
B1=0.22;                   #magnetic field in the main chamber(T)
m2=13;                     #mass number of carbon(kg)
m1=12;                     #mass number of carbon(kg)
e=1.6*10**-9;
q=1.67*10**-27;

#Calculation                        
v=E/B;                     #velocity of particles(m/s)
s=((2*v*(m2-m1)*q)/(e*B1))*10**12;       #seperation on photographic plate(cm)

#Result
print "the seperation on photographic plate is",round(s,3),"cm"
the seperation on photographic plate is 1.318 cm

Example number 7.9, Page number 134

In [24]:
#importing modules
import math
from __future__ import division

#Variable declaration
v=5.6*10**6;                  #speed of the electron(m/s)
m=9.1*10**-31;                #mass of electron(kg)
e=1.6*10**-19;
s=0.03;                       #distance travelled(m)

#Calculation                        
E=(m*(v)**2)/(2*e*s);         #intensity of electric field(N/C)

#Result
print "The intensity of electric field is",round(E),"N/C"
The intensity of electric field is 2973.0 N/C

Example number 7.10, Page number 134

In [27]:
#importing modules
import math
from __future__ import division

#Variable declaration
v=5*10**7;
B=0.4;                   #magnetic field(T)
r=0.711*10**-3;          #radius of the circle(m)

#Calculation                        
Q=v/(B*r);               #charge to mass ratio(C/kg)

#Result
print "The charge to mass ratio is",round(Q/10**10,2),"*10**10 C/kg"
The charge to mass ratio is 17.58 *10**10 C/kg

Example number 7.11, Page number 135

In [29]:
#importing modules
import math
from __future__ import division

#Variable declaration
m=9.1*10**-31;              #mass of electron(kg)
v=3*10**7;                  #speed of electron(m/s)
R=0.05;                     #radius of the circle(m)
q=1.6*10**-31;

#Calculation                        
B=((m*v)/(q*R))*10**-9;          #magnetic field(mT)

#Result
print "The magnetic field to bend a beam is",round(B,1),"mT"
The magnetic field to bend a beam is 3.4 mT

Example number 7.12, Page number 135

In [31]:
#importing modules
import math
from __future__ import division

#Variable declaration
m=9.1*10**-31;                #mass of electron(kg)
q=1.6*10**-19;
t=8*10**-9;                   #time(ns)

#Calculation                        
B=(2*math.pi*m*500)/(q*t);          #magnetic field(T)

#Result
print "The magnetic field is",round(B,2),"T"
The magnetic field is 2.23 T

Example number 7.13, Page number 135

In [33]:
#importing modules
import math
from __future__ import division

#Variable declaration
v=9.15*10**7;                  #cyclotron frequency of proton(Hz)
m=1.67*10**-27;                #mass of proton(kg)
q=1.6*10**-19;

#Calculation                        
B=(2*math.pi*v*m)/q;           #magnetic field(T)

#Result
print "The magnetic field is",int(B),"T"
The magnetic field is 6 T