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"
```

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"
```

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"
```

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"
```

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"
```

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"
```

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"
```

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"
```

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"
```

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"
```

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"
```

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"
```

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"
```

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"
```

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"
```