# Chapter 9 Motion of charged particles in electric and magnetic motion¶

## Example 9.1 Page no 472¶

In [9]:
#Given
V=90                          #V
d=2.0*10**-2
e=1.8*10**11
x=5*10**-2
v=10**7

#Calculation
E=V/d
a=e*E
t=x/v
y=0.5*a*t**2

#Result
print"Transverse deflection produced by electric field is", round(y*10**2,1),"cm"

Transverse deflection produced by electric field is 1.0 cm


## Example 9.2 Page no 473¶

In [31]:
#Given
V=500
d=2*10**-2                #m
v=3*10**7
x=6*10**-2

#Calculation
import math
E=V/d
a=E*e
t=x/v
v1=a*t
T=v1/v
A=math.atan(T)*180.0/3.14

#Result
print"Angle is", round(A,1),"degree"

Angle is 16.7 degree


## Example 9.3 Page no 474¶

In [34]:
#Given
x=10*10**-2
v=3*10**7
S=1.76*10**-3
a=1800

#Calculation
t=x/v
e=S*2/(a*t**2)

#Result
print"Specific charge of the electron is", e,"C/Kg"

Specific charge of the electron is 1.76e+11


## Example 9.4 Page no 478¶

In [44]:
#Given
m=9*10**-31
v=3*10**7
q=1.6*10**-19                         #C
B=6*10**-4

#Calculation
import math
r=m*v/(q*B)
f=q*B/(2.0*math.pi*m)
E=(0.5*m*v**2)/1.6*10**-16

#Result
print"Energy is", round(E*10**32,2),"Kev"

Energy is 2.53 Kev


## Example 9.5 Page no 479¶

In [50]:
#Given
m=9*10**-31
e=1.6*10**-19
V=100
B=0.004

#Calculation
import math
r=math.sqrt(2*m*e*V)/(e*B)

#Result
print"Radius of the path is", round(r*10**3,1),"mm"

Radius of the path is 8.4 mm


## Example 9.6 Page no 479¶

In [70]:
#Given
m=1.67*10**-27
v=4*10**5
a=60
q=1.6*10**-19
B=0.3

#Calculation
import math
r=(m*v*math.sin(a*3.14/180.0))/q*B
P=v*math.cos(a*3.14/180.0)*((2*math.pi*m)/(q*B))

#Result
print"(i) Radius of the helical path is",round(r*10**3,1),"cm"
print"(ii) Pitch of helix is", round(P*10**2,2),"cm"

(i) Radius of the helical path is 1.1 cm
(ii) Pitch of helix is 4.38 cm


## Example 9.7 Page no 479¶

In [78]:
#Given
M=5*10**6               #ev
e=1.6*10**-19
m=1.6*10**-27
B=1.5

#Calculation
import math
v=math.sqrt((2*M*e)/m)
F=q*v*B*math.sin(90*3.14/180.0)

#Result
print"Magnitude of the force is", round(F*10**12,2)*10**-12,"N"

Magnitude of the force is 7.59e-12 N


## Example 9.8 Page no 480¶

In [10]:
#Given
m=1.67*10**-27                       #Kg
v=4*10**5
B=0.3                           #T
q=1.6*10**-19                      #C

#Calculation
import math
r=m*v*math.sin(60*3.14/180.0)/(q*B)
P=2*math.pi*r*1/(math.tan(60*3.14/180.0))

#Result
print"Pitch of the helix is", round(P*10**2,2),"cm"

Pitch of the helix is 4.38 cm
Radius of helical path is 1.205 cm


## Example 9.9 Page no 480¶

In [15]:
#Given
q=3.2*10**-19
B=1.2
r=0.45
m=6.8*10**-27

#Calculation
import math
v=(q*B*r)/m
f=v/(2.0*math.pi*r)
K=(0.5*m*v**2)/(1.6*10**-19)
V=K/2.0

#Result
print"Required potentila difference is", round(V*10**-6,0),"*10**6 V"

Required potentila difference is 7.0 *10**6 V


## Example 9.10 Page no 480¶

In [20]:
#Given
I=4
u=10**-7
a=0.2                           #m
v=4*10**6
q=1.6*10**-19

#Calculation
B=(u*2*I)/a
F=q*v*B

#Result
print"Force is", F,"N"

Force is 2.56e-18 N


## Example 9.11 Page no 481¶

In [22]:
#Given
e=1.6*10**-19
a=10**6

#Calculation
q=2*e
F=q*a

#Result
print"Magnitude force acting on the particle is", F

Magnitude force acting on the particle is 3.2e-13


## Example 9.13 Page no 482¶

In [29]:
#Given
E=3.4*10**4                        #V/m
B=2*10**-3                         #Wb/m**2
m=9.1*10**-31
e=1.6*10**-19

#Calculation
v=E/B
r=(m*v)/(e*B)

#Result
print"Radius of the circular path is", round(r*10**2,1),"*10**-2 m"

Radius of the circular path is 4.8 *10**-2 m


## Example 9.14 Page no 482¶

In [32]:
#Given
V=600                            #V
d=3*10**-3                                    #m
v=2*10**6                                   #m/s

#Calculation
B=V/(d*v)

#Result
print"Magnitude of magnetic field is", B,"T"

Magnitude of magnetic field is 0.1 T


## Example 9.15 Page no 487¶

In [45]:
#Given
q=1.6*10**-19                          #c
B=2                                    #T
m=1.66*10**-27                         #Kg
K=5*10**6

#Calculation
import math
f=(q*B)/(2.0*math.pi*m)
v=math.sqrt((2*K*q)/m)
r=(m*v)/(q*B)

#Result
print"(i) The frequency needed for applied alternating voltage is", round(f*10**-7,0),"*10**7 HZ"
print"(ii) Radius of the cyclotron is",round(r,2),"m"

(i) The frequency needed for applied alternating voltage is 3.0 *10**7 HZ
(ii) Radius of the cyclotron is 0.16 m


## Example 9.16 Page no 487¶

In [51]:
#Given
B=1.7                  #T
q=1.6*10**-19          #c
r=0.5
m=1.66*10**-27

#Calculation
K=((B**2*q**2*r**2)/(2.0*m))/q

#Result
print"Kinetic energy of proton is", round(K*10**-6,0),"Mev"

Kinetic energy of proton is 35.0 Mev


## Example 9.17 Page no 487¶

In [61]:
#Given
B=0.8
q=3.2*10**-19                #C
d=1.2
m=4*1.66*10**-27               #Kg
a=1.60*10**-19

#Calculation
import math
r=d/2.0
K=(B**2*q**2*r**2)/(2.0*m*a)
v=(q*B*r)/m
f=(q*B)/(2.0*math.pi*m)

#Result
print"Frequency of alternating voltage is", round(f*10**-7,2),"*10**7 HZ"

Frequency of alternating voltage is 0.61 *10**7 HZ


## Example 9.18 Page no 488¶

In [67]:
#Given
q=1.6*10**-19               #C
r=0.6                        #m
m=1.67*10**-27               #Kg
f=10**7

#Calculation
import math
B=(2*math.pi*m*f)/q
K=((B**2*q**2*r**2)/(2.0*m))/1.6*10**-13

#Result
print"Kinetic energy of the protons is", round(K*10**26,1),"Mev"

Kinetic energy of the protons is 7.4 Mev


## Example 9.19 Page no 493¶

In [71]:
#Given
I=5                     #A
l=0.06                   #m
B=0.02                   #T
a=90

#Calculation
import math
F=I*B*l*math.sin(a*3.14/180.0)

#Result
print"Force is", round(F,3),"N"

Force is 0.006 N


## Example 9.20 Page no 494¶

In [76]:
#Given
m=0.2                        #Kg
I=2                          #A
l=1.5                        #m
g=9.8

#Calculation
B=(m*g)/(I*l)

#Result
print"Magnitude of the magnetic field is", round(B,2),"T"

Magnitude of the magnetic field is 0.65 T


## Example 9.21 Page no 494¶

In [82]:
#given
r=0.002                  #m
m=0.05
g=9.8

#Calculation
u=4*math.pi*10**-7
f=u/(2*math.pi*r)
f1=m*g
I=math.sqrt(f1*f**-1)

#Result
print"Current in each wire is", I,"A"

Current in each wire is 70.0 A


## Example 9.22 Page no 494¶

In [89]:
#Given
r=0.04                   #m
I1=20
I2=16
l=0.15
r1=0.1

#Calculation
import math
u=4*math.pi*10**-7
F1=(u*I1*I2*l)/(2.0*math.pi*r)
F2=(u*I1*I2*l)/(2.0*math.pi*r1)
F=F1-F2

#Result
print"Net force on the loop is", F*10**4,"*10**-4 N"

Net force on the loop is 1.44 *10**-4 N


## Example 9.23 Page no 495¶

In [94]:
#Given
m=0.3                #Kg
a=30                  #degree
B=0.15                #T
g=9.8                 #m/s**2

#Calculation
import math
I=(m*g*math.tan(a*3.14/180.0))/B

#Result
print"value of current is", round(I,2),"A"

value of current is 11.31 A


## Example 9.24 Page no 495¶

In [99]:
#Given
B=3*10**-5                #T
I=1                       #A

#Calculation
F=I*B*math.sin(90)

#Result
print"The direction of the force is downward i.e", round(F*10**5,0),"*10**-5 N/m"

The direction of the force is downward i.e 3.0 *10**-5 N/m

In [ ]:
Example 9.25 Page no 495

In [105]:
#Given
m=1.2*10**-3
B=0.6                       #T
g=9.8                        #m/s**2
r=0.05
b=3.8

#Calculation
I=(m*g)/B
R=r*b
V=I*R

#Result
print"Potentila difference is", round(V*10**3,1),"*10**-3 V"

Potentila difference is 3.7 *10**-3 V


## Example 9.26 Page no 496¶

In [109]:
#Given
I2=10                       #A
r=0.1                        #m
l=2                          #m
I1=2
I2=10
r=0.1

#Calculation
u=4*math.pi*10**-7
F=u*I1*I2*I1/(2.0*math.pi*r)

#Result
print"Force on small conductor", F,"N"

Force on small conductor 8e-05 N


## Example 9.27 Page no 500¶

In [121]:
#Given
A=10**-3                     #m**
n=10
I=2                        #A
B=0.1                     #T

#Calculation
import math
t=n*I*A*B*math.cos(0)
t1=n*I*A*B*math.cos(60*3.14/180.0)

#Result
print"(i) Torque when magnetic field is parallel to the field", round(t*10**3,0),"*10**-3 Nm"
print"(ii) Torque when magnetic field is perpendicular to the field is zero"
print"(iii) Torque when magnetic field is 60 degree to the field is",round(t1*10**3,1),"*10**-3 Nm"

(i) Torque when magnetic field is parallel to the field 2.0 *10**-3 Nm
(ii) Torque when magnetic field is perpendicular to the field is zero
(iii) Torque when magnetic field is 60 degree to the field is 1.0 *10**-3 Nm


## Example 9.28 Page no 500¶

In [127]:
#Given
r=7
I=10
B=100*10**-4

#Calculation
import math
A=math.pi*r**2
t=I*A*B

#Result
print"Magnitude of maximum torque is", round(t*10**-1,2),"*10**-3 Nm"

Magnitude of maximum torque is 1.54 *10**-3 Nm


## Example 9.29 Page no 501¶

In [134]:
#Given
N=10
I=0.06
r=0.05
n=1000
I2=25

#Calculation
import math
A=math.pi*r**2
M=N*I*A
u=4*math.pi*10**-7
B=u*n*I2
t=M*B*math.sin(45*3.14/180.0)

#Result
print"Torgue is", round(t*10**4,2),"*10**-4 Nm"

Torgue is 1.05 *10**-4 Nm


## Example 9.30 Page no 501¶

In [25]:
#Given
n=100
l=3.2
r=0.1

#Calculation
import math
u=4*math.pi*10**-7
B=(u*n*l)/(2.0*r)
M=n*l*math.pi*r**2
t=M*B*math.sin(0)
t1=(M*B*math.sin(90*3.14/180.0))*10**3
w=math.sqrt((2*M*B*10**3)/r)

#Result
print"(a) Field at the centre of the coil is", round(B*10**3,0),"*10**-3 T"
print"(b) Magnetic moment of the coil is",round(M,0),"Am**2"
print"(c) Magnitude of the torque on the coil in the initial position is",t
print" Magnitude of the torque on the coil in the final position is",round(t1,0),"Nm"
print "(d) Angular speed acquired by the coil is",round(w,0),"rad/s"

(a) Field at the centre of the coil is 2.0 *10**-3 T
(b) Magnetic moment of the coil is 10.0 Am**2
(c) Magnitude of the torque on the coil in the initial position is 0.0
Magnitude of the torque on the coil in the final position is 20.0 Nm
(d) Angular speed acquired by the coil is 20.0 rad/s


## Example 9.31 Page no 505¶

In [32]:
#Given
n=125
I=20*10**-3                       #A
B=0.5                             #T
A=400*10**-6                       #m**2
K=40*10**-6

#Calculation
T=n*I*B*A
a=T/K

#Result
print"(i) Torque exerted is", T*10**4,"*10**-4 Nm"
print"(ii) Angular deflection of the coil is", a,"degree"

(i) Torque exerted is 5.0 *10**-4 Nm
(ii) Angular deflection of the coil is 12.5 degree


## Example 9.32 Page no 505¶

In [36]:
#Given
K=3*10**-9                            #Nm/deg
a=36
n=60
B=9*10**-3                              #T
A=5*10**-5                                  #m**2

#Calculation
I=(K*a)/(n*B*A)

#Result
print"Maximum current is", I*10**3,"mA"

Maximum current is 4.0 mA


## Example 9.33 Page no 506¶

In [39]:
#Given
n=30
B=0.25                      #T
A=1.5*10**-3
K=10**-3

#Calculation
S=(n*B*A)/K

#Result
print"Current sensitivity of the galvanometer is", S,"degree/A"

Current sensitivity of the galvanometer is 11.25 degree/A


## Example 9.35 Page no 509¶

In [47]:
#Given
Ig=0.015               #A
G=5
I=1
V=15

#Calculation
S=(Ig*G)/(I-Ig)
R=G*S/(G+S)
R1=(V/Ig)-G
R2=R1+G

#Result
print"(i) Resistance of ammeter of range 0-1 A is", R,"ohm"
print"(ii) Resistance of ammeter of range 0-15 A is", R2,"ohm"

(i) Resistance of ammeter of range 0-1 A is 0.075 ohm
(ii) Resistance of ammeter of range 0-15 A is 1000.0 ohm


## Example 9.36 Page no 510¶

In [58]:
#Given
V=75                #mV
Ig=0.025              #A
I=25                     #mA
I1=100
V1=750

#Calculation
G=V/I
S=(Ig*G)/(I1-Ig)
R=(V1/Ig)-G

#Result
print"(i) Resistance for an ammeter of range 0-100 A is", round(S,5),"ohm"
print"(ii) Resistance for an ammeter of range 0-750 A is", round(R,5),"ohm"

(i) Resistance for an ammeter of range 0-100 A is 0.00075 ohm
(ii) Resistance for an ammeter of range 0-750 A is 29997.0 ohm


## Example 9.37 Page no 510¶

In [74]:
#Given
Rg=60
R1=3.0
rs=0.02

#Calculation
Rt=Rg+R1
I=R1/Rt
Rm=(Rg*rs)/(Rg+rs)
R2=Rm+R1
I1=R1/R2
I2=R1/R1

#Result
print"(i) The value of current is", round(I,3),"A"
print"(ii) The value of current is", round(I1,2),"A"
print"(iii) The value of current is",I2,"A"

(i) The value of current is 0.048 A
(ii) The value of current is 0.99 A
(iii) The value of current is 1.0 A


## Example 9.38 Page no 511¶

In [77]:
#Given
V=100
v=1
a=1980

#Calculation
Rm=a/(V-v)

#Result
print"Resistance of the voltmeter is", Rm,"ohm"

Resistance of the voltmeter is 20 ohm


## Example 9.39 Page no 511¶

In [84]:
#Given
R1=1200.0                         #ohm
R2=600                          #ohm
Vab=5                           #V
V=35

#Calculation
Rp=(R1*R2)/(R1+R2)
I=Vab/Rp
pd=V-Vab
R=pd/I

#Result
print"value of unknown resistance is", R,"ohm"

value of unknown resistance is 2400.0 ohm


## Example 9.40 Page no 511¶

In [95]:
#Given
R1=400                      #ohm
R2=800.0
R3=10
V=6
R11=10000.0
R22=400

#Calculation
Rt=R1+R2+R3
I=V/Rt
Rp=(R11*R22)/(R11+R22)
R=Rp+800
I1=V/R
Vab=I1*Rp

#Result
print"Hence the voltmeter will read", round(Vab,2),"V"

Hence the voltmeter will read 1.95 V


## Example 9.41 Page no 512¶

In [101]:
#Given
V=2                               #V
R=2000.0                           #ohm

#Calculation
I=V/R
pd=I*R

#Result

Reading of ammeter is 1.0 mA
Reading of voltmeter is 2.0 V


## Example 9.42 Page no 512¶

In [108]:
#Given
E=3
G=100
R=200.0
n=30

#Calculation
Ig=E/(G+R)
K=(Ig/n)*10**6

#Result
print"Figure of merit of the galvanometer is", round(K,1),"micro A/division"

Figure of merit of the galvanometer is 333.3 micro A/division


## Example 9.43 Page no 513¶

In [115]:
#Given
V1=60                   #ohm
V2=30
R=300.0
R1=1200
R2=400                       #ohm

#Calculation
V=V1-V2
I=V/R
R11=(R1*R)/(R1+R)
I=V1/(R11+R2)
V11=I*R11

#Result

Voltmeter will read 22.5 V


## Example 9.44 Page no 513¶

In [123]:
#Given
R=20.0                   #K ohm
R2=1                     #K ohm

#Calculation
Vr=(R*R2)/(R+R2)

#Result
print"(i) Voltmeter resistance is", R,"K ohm"
print"(ii) Voltmeter resistance is",R2,"K ohm"
print"(iii) Voltmeter resistance is",round(Vr,2),"K ohm"

(i) Voltmeter resistance is 20.0 K ohm
(ii) Voltmeter resistance is 1 K ohm
(iii) Voltmeter resistance is 0.95 K ohm


## Example 9.45 Page no 514¶

In [128]:
#Given
s=20*10**-6
n=30
I=1                    #A
G=25                    #ohm

#Calculation
Ig=s*n
S=Ig*G/(1-Ig)
Ra=G*S/(G+S)

#Result
print"Resistance of ammeter is",Ra,"ohm"

Resistance of ammeter is 0.015 ohm