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"
print"Radius of helical path is",round(r*10**2,3),"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
print"Reading of ammeter is", I*10**3,"mA \nReading of voltmeter is",pd,"V"

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
print"Voltmeter will read", V11,"V"

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