# Chapter 12 Motion of charged particle¶

## Example 12.1 Page no 379¶

In [7]:
#Given
m=1.6*10**-27                       #Kg
e=1.6*10**-19
Ey=2*10**4                           #V/m
x=0.1                                #m
vx=5*10**6                           #m/s

#Calculation
t=x/vx
Fy=e*Ey
a=Fy/m
y=a*t**2/2.0

#Result
print"Transverse deflection is", y*10**3,"mm"

Transverse deflection is 0.4 mm


## Example 12.2 Page no 379¶

In [11]:
#Given
n=8*10**28                        #/m**2
l=1                                #m
A=8*10**-6                          #m**2
B=5*10**-3                         #T
F=8*10**-2                         #N
e=1.6*10**-19                       #C

#Calculation
vd=F/(B*n*A*l*e)

#Result
print"Drift velocity is", vd*10**4,"*10**-4 m/s"

Drift velocity is 1.5625 *10**-4 m/s


## Example 12.3 Page no 379¶

In [14]:
#Given
q=1.6*10**-19                           #C
v=10**7                                  #m/s
B=3                                      #T

#Calculation
F=q*v*B

#Result
print"Instantaneous force is", F,"N"

Instantaneous force is 4.8e-12 N


## Example 12.4 Page no 379¶

In [6]:
#Given
I=2                              #A
a=0.1                            #m
u=10**-7
q=1.6*10**-19
v=4*10**4                        #m/s

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

#Result
print"Force of magnetic field is", F,"N"

Force of magnetic field is 2.56e-20 N


## Example 12.6 Page no 380¶

In [10]:
#Given
v=10**5                        #m/s
e=1.6*10**-19                  #C
m=9.1*10**-31                    #Kg
B=0.019*10**-4                   #T

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

#Result
print"Radius of the circular path is", round(r,3),"m"

Radius of the circular path is 0.299 m


## Example 12.7 Page no 380¶

In [16]:
#Given
e=1.6*10**-19
m=9*10**-31                                #Kg
T=10**-6                                    #S

#Calculation
import math
B=2*math.pi*m/(e*T)

#Result
print"Magnetic field is", round(B*10**5,3)*10**-5 ,"T"

Magnetic field is 3.534e-05 T


## Example 12.9 Page no 381¶

In [25]:
#Given
m=1.67*10**-27                       #Kg
e=1.60*10**-19
V=10**7                                #Hz
R=0.6                                 #m

#Calculation
import math
B=2*math.pi*m*V/e
Emax=(B**2*e**2*R**2/(2*m))/1.6*10**13

#Result
print"Kinetic energy of the proton is",round(Emax,3),"Mev"

Kinetic energy of the proton is 7.417 Mev


## Example 12.10 Page no 381¶

In [29]:
#Given
I=5                                  #A
l=0.1                                 #m
m=3*10**-3
g=9.8
a=0.5

#Calculation
w=m*g*l
B=w/a

#Result
print"Magnitude of the magnetic field is", B*10**3,"*10**-3 tesla"

Magnitude of the magnetic field is 5.88 *10**-3 tesla


## Example 12.11 Page no 381¶

In [33]:
#given
I1=4                            #A
I2=6
r=0.03                           #m
u=10**-7

#Calculation
F=u*2*I1*I2/r

#Result
print"Force per unit length is", F*10**4,"*10**-4 N/m"

Force per unit length is 1.6 *10**-4 N/m


## Example 12.12 Page no 381¶

In [38]:
#Given
I1=5                             #A
I2=12
r=0.4                            #m
u=10**-7

#Calculation
F=u*2*I1*I2/r
F1=u*2*I1*I2/r

#Result
print"(i) Force when current flows in same direction is", F,"N/m"
print"(ii) Force when current flows in opposite direction is",F1,"N/m"

(i) Force when current flows in same direction is 3e-05 N/m
(ii) Force when current flows in opposite direction is 3e-05 N/m


## Example 12.13 Page no 381¶

In [40]:
#Given
I1=300                          #A
r=1.5*10**-2                    #m
u=10**-7

#Calculation
F=u*2*I1*I1/r

#Result
print"Force per unit length is",F,"N/m"

Force per unit length is 1.2 N/m


## Example 12.14 Page no 381¶

In [44]:
#Given
I=10                       #A
n=100
A=8*10**-2                  #m**2
B=5                         #T

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

#Result
print"Torque is", round(t,0),"Nm"

Torque is 200.0 Nm


## Example 12.15 Page no 381¶

In [50]:
#Given
n=30
I=6                        #A
B=1                           #T
r=8*10**-2                     #m

#Calculation
import math
A=math.pi*r**2
t=n*B*I*A*math.sin(60*3.14/180.0)

#Result
print"(a) Magnitude of the counter torque is", round(t,3),"Nm"
print"(b) Torque on the planar loop is independent of its shape, the torque will remain unchanged."

(a) Magnitude of the counter torque is 3.133 Nm
(b) Torque on the planar loop is independent of its shape, the torque will remain unchanged.


## Example 12.16 Page no 382¶

In [62]:
#Given
B=100*10**-4                             #T
I=10                                     #A
l=44

#Calculation
import math
r=l/(2.0*math.pi)
A=math.pi*r**2
t=B*I*A

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

Maximum torque is 1.54 *10**-3 Nm


## Example 12.17 Page no 382¶

In [68]:
#Given
n=20
r=10*10**-2                          #m
B=0.10                               #T
I=5                                   #A
n1=10**29                             #/m**3
A1=10**-5                             #m**2

#Calculation
import math
A=math.pi*r**2
t=n*B*I*A*math.sin(0*3.14/180.0)
F=B*I/(n1*A1)

#Result
print"(a) Total torque on the coil is", t
print"(b) Net force on a planar loop in a magnetic field is always zero"
print"(c) Average force is",F,"N"

(a) Total torque on the coil is 0.0
(b) Net force on a planar loop in a magnetic field is always zero
(c) Average force is 5e-25 N


## Example 12.18 Page no 382¶

In [70]:
#Given
A=5*10**-4                          #m**2
n=60
a=18                                 #degree
B=90*10**-4                          #T
I=0.20*10**-3                        #A

#calculation
k=n*B*I*A/a

#Result
print"Torsional constant is",k,"N m per degree"

Torsional constant is 3e-09 N m per degree


## Example 12.21 Page no 383¶

In [74]:
#Given
G=15                           #ohm
Ig=2*10**-3                    #A
I=5                            #A

#Calculation
S=Ig*G/(I-Ig)

#Result
print"Shunt resistance is",round(S,3),"Ohm"

Shunt resistance is 0.006 Ohm


## Example 12.22 Page no 383¶

In [79]:
#Given
V=50*10**-3                          #V
G=100.0                                #ohm

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

#Result
print"Shunt resistance is", round(S,2),"ohm"

Shunt resistance is 0.01 ohm


## Example 12.23 Page no 383¶

In [80]:
#Given
G=100                          #ohm
Ig=5*10**-3                    #A
I=5                            #A

#Calculation
S=Ig*G/(I-Ig)

#Result
print"Shunt resistance is",S

Shunt resistance is 0.1001001001


## Example 12.24 Page no 383¶

In [88]:
#Given
G=5                          #ohm
Ig=15.0*10**-3                   #A
I=1.5
V=1.5                          #V

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

#Result
print"(a) To enable galvanometer to read 1.5 A is", round(S,2),"ohm"
print"(b) To enable galvanometer to read 1.5 V is",R,"ohm"

(a) To enable galvanometer to read 1.5 A is 0.05 ohm
(b) To enable galvanometer to read 1.5 V is 95.0 ohm


## Example 12.25 Page no 383¶

In [95]:
#Given
G=10                        #ohm
Ig=25.0*10**-3                #A
V=120                       #V
I=20                         #A

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

#Result
print"(a) To convert the galvanometer into the voltmeter reading is" ,R,"ohm"
print"(b) To convert the galvanometer into the ammeter reading is",round(S,4),"ohm"

(a) To convert the galvanometer into the voltmeter reading is 4790.0 ohm
(b) To convert the galvanometer into the ammeter reading is 0.0125 ohm


## Example 12.26 Page no 383¶

In [98]:
#Given
E=3                           #v
R=55                             #ohm
Ra=1
I=50*10**-3                     #A

#Calculation
r=(E/I)-(R+Ra)

#Result
print"Value of r is", r,"ohm"

Value of r is 4.0 ohm


## Example 12.27 Page no 384¶

In [108]:
#Given
E=60                          #V
R1=400                        #ohm
R2=300
V1=30.0
a=120000

#Calculation
Rv=(-V1*a)/(V1*(R1+R2)-E*R1)
R=Rv*R2/(Rv+R2)
I1=E/(R+R1)
V=I1*R

#Result

Voltmeter reads 22.5 V


## Example 12.28 Page no 384¶

In [122]:
#Given
Rv=400.0
E=84                                #V
r=100.0
r1=200

#Calculation
R=1/(1/Rv+1/100.0)
R1=R+200
I=E/R1
I1=I/5.0
V=I1*Rv
R2=r+r1
I2=E/R2
V2=I2*r

#Result
print"(a) Reading on voltmeter is", V,"V"
print"(b) Potential difference is",V2,"V"

(a) Reading on voltmeter is 24.0 V
(b) Potential difference is 28.0 V


## Example 12.29 Page no 385¶

In [131]:
#Given
E=120                             #v
Rv=10**4                          #ohm
a=4.0

#Calculation
x=(Rv*(E-a))/a

#Result
print"Large resistance is", x*10**-3,"K ohm"

Large resistance is 290.0 K ohm


## Example 12.30 Page no 385¶

In [127]:
#Given
B=0.75                          #T
E=9*10**5                        #V/m
V=15*10**3

#Calculation
v=E/B
a=v**2/(2.0*V)

#Result
print"The value of e/m is", a*10**-7,"*10**7 C/Kg"

The value of e/m is 4.8 *10**7 C/Kg


## Example 12.31 Page no 385¶

In [153]:
#Given
m=9.11*10**-31                           #Kg
e=1.60*10**-19                           #C
B=0.40*10**-4                             #T
a=18*1.6*10**-16
PQ=0.30
a2=1.52                                  #degree

#calculation
import math
r=math.sqrt(2*m*a)/(B*e)
a1=(PQ/r)
PA=r*(1-math.cos(a2*3.14/180.0))

#Result
print"up and down deflection of the beam is", round(PA*10**3,0),"mm"

up and down deflection of the beam is 4.0 mm


## Example 12.32 Page no 386¶

In [161]:
#Given
m=60*10**-3
g=9.8
I=5
l=0.45

#Calculation
B=m*g/(I*l)
T=2*m*g

#Result
print"(i) Magnetic field is", round(B,3),"T"
print"(ii) Total tension in the wire is",T,"N"

(i) Magnetic field is 0.261 T
(ii) Total tension in the wire is 1.176 N


## Example 12.33 Page no 386¶

In [165]:
#Given
B=0.15                         #T
m=0.30                          #Kg/m
a=30                              #degree
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 12.34 Page no 386¶

In [171]:
#Given
I1=4                           #A
I2=3
r=3.0*10**-2                      #m
u=10**-7
l=5*10**-2

#Calculation
F=u*2*I1*I2/r
F1=F*l

#Result
print"Total force is", F1,"N (attractive force)"

Total force is 4e-06 N (attractive force)


## Example 12.35 Page no 386¶

In [182]:
#Given
AB=25*10**-2                         #m
BC=10*10**-2
r1=2.0*10**-2                        #m
I1=15                                #A
I2=25                                 #A
u=10**-7

#Calculation
r2=BC+r1
F1=u*2*I1*I2*AB/r1
F2=u*2*I1*I2*AB/r2
F=F1-F2

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

Net force on the loop is 7.8125 *10**-4 N (towards XY)


## Example 12.36 Page no 387¶

In [186]:
#Given
M=30*10**-3                         #Kg
g=9.8                                #m/s**2
l=0.5                                #m
r=10**-2
u=10**-7

#Calculation
import math
I=math.sqrt((M*g*r)/(u*2*l))

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

Value of current is 171.46 A


## Example 12.37 Page no 387¶

In [197]:
#Given
n=900
l=0.6
u=10**-7
l2=0.02                                   #m
l1=6
m=2.5*10**-3                               #Kg
g=9.8

#Calculation
import math
n1=n/l
B=4*math.pi*n1
F=B*l1*l2
I=m*g/F

#Result
print"Current in the winding of the secondary is", round(I*10**7,1),"A"

Current in the winding of the secondary is 108.3 A


## Example 12.38 Page no 387¶

In [204]:
#Given
A=1.6*10**-3                          #m**2
n=200
B=0.2                                  #T
a=30                                    #degree
K=10**-6                                 #N m /degree
a1=0.1

#Calculation
Imax=K*a/(n*B*A)
Imin=K*a1/(n*B*A)

#Result
print"(i) Minimum current is",round(Imax*10**4,2),"*10**-4 A"
print"(ii) Smallest current that can be detected is",Imin,"A"

(i) Minimum current is 4.69 *10**-4 A
(ii) Smallest current that can be detected is 1.5625e-06 A


## Example 12.39 Page no 388¶

In [212]:
#Given
R=5000.0                                  #ohm/V
V=5
V1=20.0

#Calculation
Ig=1/R
G=V/Ig
R1=(V1/Ig)-G
Rn=R1+G
Rv=Rn/V1

#Result
print"New voltmeter will be still graded as", Rv,"ohm/V"

New voltmeter will be still graded as 5000.0 ohm/V


## Example 12.40 Page no 388¶

In [215]:
#Given
V1=100                         #V
Rv=400.0

#Calculation
I1=V1/Rv
V=I1*20
V2=V1+V
V3=V2-V1

#Result
print"Error in the reading of the voltmeter is",V3,"V"

Error in the reading of the voltmeter is 5.0 V