# 7: Electromagnetic Induction¶

## Example number 7.1, Page number 204¶

In [13]:
#importing modules
import math
from __future__ import division

#Variable declaration
R=125;     #resistance(ohm)
V=3*10**-4;    #potential difference(V)
T=10;   #time period(sec)
theta1=16*10**-2;    #deflection(m)
theta=5*10**-2;    #deflection(m)

#Calculation
i=V/R;     #current(A)
q=T*i*theta/(2*math.pi*theta1);    #charge(C)

#Result
print "charge is",round(q*10**6,3),"*10**-6 C"

charge is 1.194 *10**-6 C


## Example number 7.2, Page number 205¶

In [15]:
#importing modules
import math
from __future__ import division

#Variable declaration
T=8;     #time period(s)
i=2*10**-6;    #current(A)
theta1=1;
theta=1;

#Calculation
q=T*i*theta/(2*math.pi*theta1);    #charge(C)

#Result
print "charge is",round(q*10**6,3),"*10**-6 C"
print "answer varies due to rounding off errors"

charge is 2.546 *10**-6 C
answer varies due to rounding off errors


## Example number 7.3, Page number 205¶

In [22]:
#importing modules
import math
from __future__ import division

#Variable declaration
l=1.8*10**-2;    #length(m)
B=0.5;   #magnitude of field(Wb/m**2)
N=200;   #number of turns
t=0.8;   #time period(sec)
R=12;    #resistance(ohm)

#Calculation
A=l**2;    #area of coil(m**2)
phiB=B*A;   #magnetic flux in coil(Wb)
e=N*(phiB-0)/t;    #induced emf(V)
i=e/R;    #current(A)

#Result
print "induced emf is",e,"V"
print "current is",i*10**4,"*10**-4 A"
print "answers given in the book are wrong"

induced emf is 0.0405 V
current is 33.75 *10**-4 A
answers given in the book are wrong


## Example number 7.6, Page number 207¶

In [24]:
#importing modules
import math
from __future__ import division

#Variable declaration
B=100*10**-4;    #magnetic field(Wb/m**2)
d=20*10**-2;    #diameter(m)
n=10;   #number of rotations

#Calculation
dAbydt=math.pi*n*(r**2);   #area(turns m**2/s)
e=B*dAbydt;     #potential difference(V)

#Result
print "potential difference is",round(e*10**3,3),"mV"

potential difference is 3.142 mV


## Example number 7.7, Page number 207¶

In [25]:
#importing modules
import math
from __future__ import division

#Variable declaration
l=1;    #length(m)
B=0.2;   #magnetic field(Wb/m**2)
v=0.8;   #velocity(m/s)

#Calculation
e1=B*l*v*math.sin(theta1);    #induced emf when B and v are perpendicular(V)
e2=B*l*v*math.sin(theta1)*math.sin(theta2);   #induced emf with angle 45 degrees(V)
e3=B*l*v*math.sin(theta1)*math.sin(theta2)*math.sin(theta3);    #induced emf with angle 30 degrees(V)

#Result
print "induced emf when B and v are perpendicular is",round(e1,4),"V"
print "induced emf with angle 45 degrees is",round(e2,3),"V"
print "induced emf with angle 30 degrees is",round(e3,3),"V"

induced emf when B and v are perpendicular is 0.1386 V
induced emf with angle 45 degrees is 0.098 V
induced emf with angle 30 degrees is 0.049 V


## Example number 7.8, Page number 208¶

In [26]:
#importing modules
import math
from __future__ import division

#Variable declaration
L=20;   #inductance(H)
i=0.1;   #current(A)

#Calculation
Ub=(1/2)*L*(i**2);    #energy stored in inductor(J)

#Result
print "energy stored in inductor is",Ub,"J"

energy stored in inductor is 0.1 J


## Example number 7.9, Page number 209¶

In [27]:
#importing modules
import math
from __future__ import division

#Variable declaration
e=12;    #induced emf(V)
L=53*10**-3;   #inductance(H)
R=0.35;   #resistance(ohm)

#Calculation
i=e/R;    #current(A)
Ub=(1/2)*L*(i**2);    #energy stored in inductor(J)

#Result
print "energy stored in inductor is",round(Ub,1),"J"

energy stored in inductor is 31.2 J


## Example number 7.10, Page number 209¶

In [28]:
#importing modules
import math
from __future__ import division

#Variable declaration
N=1250;    #number of turns
a=5.2*10**-2;     #length(m)
h=1.3*10**-2;     #height(m)
mew0=4*math.pi*10**-7;

#Calculation
L=(mew0*(N**2)*h*math.log(b/a))/(2*math.pi);     #inductance(H)

#Result
print "inductance is",round(L*10**3,1),"mH"

inductance is 2.4 mH


## Example number 7.11, Page number 209¶

In [29]:
#importing modules
import math
from __future__ import division

#Variable declaration
N1=500;    #number of turns
A=3*10**-3;    #area(m**2)
l=0.5;   #length(m)
mew0=4*math.pi*10**-7;
N2=8;    #number of turns

#Calculation
M=mew0*N1*N2*A/l;   #coefficient of mutual induction(H)

#Result
print "coefficient of mutual induction is",round(M*10**6),"micro H"

coefficient of mutual induction is 30.0 micro H