Chapter 9: Electromagnetic induction

Example 1, page no. 102

In [1]:
from __future__ import division
import math
#initializing  the  variables:
l  =  0.3;#  in  m
v  =  4;#  in  m/s
B  =  1.25;#  in  Tesla
R  =  20;#  in  ohms
u0  =  4*math.pi*1E-7;

#calculation:
E  =  B*l*v
I2  =  E/R

#Results
print  "\n\nResult\n\n"
print  "\n  (a)If  the  ends  of  the  conductor  are  open  circuited "
print   "no  current  will  flow  even  though  ",E,"  V  has  been  induced.\n"
print  "\n  (b)From  Ohms  law,  I  =  ",I2,"  Ampere\n"


Result



  (a)If  the  ends  of  the  conductor  are  open  circuited  no  current  will  flow  even  though   1.5   V  has  been  induced.


  (b)From  Ohms  law,  I  =   0.075   Ampere

Example 2, page no. 103

In [2]:
from __future__ import division
import math
#initializing  the  variables:
l  =  0.075;#  in  m
E  =  9;#  in  Volts
B  =  0.6;#  in  Tesla
R  =  20;#  in  ohms
u0  =  4*math.pi*1E-7;

#calculation:
v  =  E/(B*l)

#Results
print  "\n\nResult\n\n"
print  "\n  velocity  v  =  ",v,"  m/s\n"


Result



  velocity  v  =   200.0   m/s

Example 3, page no. 103

In [3]:
from __future__ import division
import math

#initializing  the  variables:
l  =  0.02;#  in  m
b  =  0.02;#  in  m
v  =  15;#  in  m/s
R  =  20;#  in  ohms
Phi  =  5E-6;#  in  Wb
u0  =  4*math.pi*1E-7;
a1  =  90;#  in  degrees
a2  =  60;#  in  degrees
a3  =  30;#  in  degrees

#calculation:
A  =  l*b
B  =  Phi/A
E90  =  B*l*v*math.sin(a1*math.pi/180)
E60  =  B*l*v*math.sin(a2*math.pi/180)
E30  =  B*l*v*math.sin(a3*math.pi/180)

#Results
print  "\n\nResult\n\n"
print  "\n  Induced  e.m.f.  at  angles  90°,  60°,  30°  are  ",(E90/1E-3),"  V,  ",round((E60/1E-3),2),"  V, "
print   "(E30/1E-3),"  V  respectively\n"


Result



  Induced  e.m.f.  at  angles  90°,  60°,  30°  are   3.75   V,   3.25   V,   1.875   V  respectively

Example 4, page no. 103

In [4]:
from __future__ import division
import math
#initializing  the  variables:
s  =  36;#  in  m
v  =  400;#  in  km/h
u0  =  4*math.pi*1E-7;
B  =  40E-6;#  in  Tesla

#calculation:
v0  =  v*5/18
E  =  B*s*v0

#Results
print  "\n\nResult\n\n"
print  "\n  Induced  e.m.f.  =  ",E,"  V\n"


Result



  Induced  e.m.f.  =   0.16   V

Example 6, page no. 105

In [5]:
from __future__ import division
import math
#initializing  the  variables:
N  =  200;#  no.  of  turns
dt  =  0.050;#  change  of  time  in  sec
u0  =  4*math.pi*1E-7;
dPhi  =  0.025;#  change  of  flux  in  Wb

#calculation:
E  =  -1*N*dPhi/dt


#Results
print  "\n\nResult\n\n"
print  "\n  Induced  e.m.f.  =  ",E,"  V\n"


Result



  Induced  e.m.f.  =   -100.0   V

Example 7, page no. 105

In [6]:
from __future__ import division
import math
#initializing  the  variables:
N  =  150;#  no.  of  turns
dt  =  0.040;#  change  of  time  in  sec
u0  =  4*math.pi*1E-7;
dPhi  =  800E-6;#  change  of  flux  in  Wb

#calculation:
#Since  the  flux  reverses,  the  flux  changes  from  C400  μWb  to  400  μWb,  a  total  change  of  flux  of  800  μWb
E  =  -1*N*dPhi/dt

#Results
print  "\n\nResult\n\n"
print  "\n  Induced  e.m.f.  =  ",E,"  V\n"


Result



  Induced  e.m.f.  =   -3.0   V

Example 8, page no. 105

In [7]:
from __future__ import division
import math
#initializing  the  variables:
L  =  12;#  in  Henry
u0  =  4*math.pi*1E-7;
dIdt  =  4;#  change  of  current  with  change  in  time  in  A/s

#calculation:
E  =  -1*L*dIdt


#Results
print  "\n\nResult\n\n"
print  "\n  Induced  e.m.f.  =  ",E,"  V\n"


Result



  Induced  e.m.f.  =   -48   V

Example 9, page no. 106

In [8]:
from __future__ import division
import math
#initializing  the  variables:
E  =  1500;#  in  Volts
dt  =  0.008;#  Change  of  time  in  sec
dI  =  4;#  change  of  current  in  A/s

#calculation:
L  =  abs(E)*dt/dI

#Results
print  "\n\n  Result  \n\n"
print  "\n  Inductance  L=  ",L,"  H\n"


  Result  



  Inductance  L=   3.0   H

Example 10, page no. 107

In [9]:
from __future__ import division
import math
#initializing  the  variables:
L  =  8;#  in  Henry
I  =  3;#  in  Amperes

#calculation:
W  =  L*I*I/2

#Results
print  "\n\n  Result  \n\n"
print  "\n  Energy  stored,  W  =  ",W,"  J\n"


  Result  



  Energy  stored,  W  =   36.0   J

Example 11, page no. 107

In [10]:
from __future__ import division
import math
#initializing  the  variables:
I  =  4;#  in  Amperes
N  =  800;#turns
Phi  =  0.005;#  in  Wb

#calculation:
L  =  N*Phi/I

#Results
print  "\n\n  Result  \n\n"
print  "\n  Inductance  L  =  ",L,"  H\n"


  Result  



  Inductance  L  =   1.0   H

Example 12, page no. 107

In [11]:
from __future__ import division
import math
#initializing  the  variables:
I1  =  3;#  in  Amperes
I2  =  0;#  in  Amperes
dt  =  0.150;#  in  secs
N  =  1500;#turns
Phi  =  0.025;#  in  Wb

#calculation:
L  =  N*Phi/I1
W  =  L*I1*I1/2
dI  =  I1  -  I2
E  =  -1*L*dI/dt

#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)Inductance  L  =  ",L,"  H\n"
print  "\n  (b)energy  stored  W  =  ",W,"  J\n"
print  "\n  (c)e.m.f.  induced  =  ",E,"  V\n"


  Result  



  (a)Inductance  L  =   12.5   H


  (b)energy  stored  W  =   56.25   J


  (c)e.m.f.  induced  =   -250.0   V

Example 13, page no. 108

In [12]:
from __future__ import division
import math
#initializing  the  variables:
I1  =  2;#  in  Amperes
I2  =  0;#  in  Amperes
dt  =  0.020;#  in  secs
N  =  750;#turns
L  =  3;#  in  Henry

#calculation:
Phi  =  L*I1/N
dI  =  I1  -  I2
E  =  -1*L*dI/dt

#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)Flux  =  ",Phi,"  Wb\n"
print  "\n  (b)e.m.f.  induced  =  ",E,"  V\n"


  Result  



  (a)Flux  =   0.008   Wb


  (b)e.m.f.  induced  =   -300.0   V

Example 14, page no. 108

In [13]:
from __future__ import division
import math
#initializing  the  variables:
dI1dt  =  200;#  change  of  current  with  change  in  time  in  A/s
N  =  2;#  no.  of  coils
E2  =  1.5;#  in  Volts

#calculation:
M  =  abs(E2)/dI1dt


#Results
print  "\n\n  Result  \n\n"
print  "\n  mutual  inductance,  M  =  ",  M,"  H\n"


  Result  



  mutual  inductance,  M  =   0.0075   H

Example 15, page no. 109

In [14]:
from __future__ import division
import math
#initializing  the  variables:
M  =  0.018;#  in  Henry
N  =  2;#  no.  of  coils
E2  =  0.72;#  in  Volts

#calculation:
dI1dt  =  abs(E2)/M

#Results
print  "\n\n  Result  \n\n"
print  "\n  rate  of  change  of  current  dI1/dt  =  ",  dI1dt,"  A/s\n"


  Result  



  rate  of  change  of  current  dI1/dt  =   40.0   A/s

Example 16, page no. 109

In [15]:
from __future__ import division
import math
#initializing  the  variables:
M  =  0.2;#  in  Henry
I1  =  10;#  in  Amperes
I2  =  4;#  in  Amperes
dt  =  0.010;#  in  secs
N  =  500;#  turns

#calculation:
dI1dt  =  (I1  -I2)/dt  
E2  =  -1*dI1dt*M
dPhi  =  abs(E2)*dt/N

#Results
print  "\n\n  Result  \n\n"
print  "\n  (a)Induced  e.m.f.  E2  =  ",  E2,"  V\n"
print  "\n  (b)change  of  flux  =  ",  dPhi,"  Wb\n"


  Result  



  (a)Induced  e.m.f.  E2  =   -120.0   V


  (b)change  of  flux  =   0.0024   Wb