# 7: Motion of a charged particle¶

## Example number 7.1, Page number 132¶

In :
#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 :
#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 :
#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
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 :
#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)

#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 :
#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
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

#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 :
#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;
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 :
#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 :
#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 :
#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 :
#importing modules
import math
from __future__ import division

#Variable declaration
v=5*10**7;
B=0.4;                   #magnetic field(T)

#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 :
#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)
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 :
#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 :
#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