```
In [1]:
```%pylab inline
%precision %.4g
from scipy import constants as c # we like to use some constants

```
```

A ferromagnetic core is shown in Figure P1-2:

```
In [2]:
```phi = 0.005 # Wb

With this current,

- What is the flux density at the top of the core?
- What is the flux density at the right side of the core?

Assume that the relative permeability of the core is:

```
In [3]:
```mu_r = 800
mu = mu_r * c.mu_0

`scipy.constants`

(see also import statement) and is simply:

```
In [4]:
```c.mu_0

```
Out[4]:
```

```
In [5]:
```l1 = 2 * 0.275 # m
l2 = 0.3 # m
l3 = 0.3 # m

```
In [6]:
```A1 = 0.05 * 0.15 # m^2
A2 = 0.05 * 0.10 # m^2
A3 = 0.05 * 0.05 # m^2

And the reluctances are hence:

```
In [7]:
```R1 = l1 / (mu * A1) # At /Wb = At/Vs
R2 = l2 / (mu * A2) # At /Wb = At/Vs
R3 = l3 / (mu * A3) # At /Wb = At/Vs
print('R1 = {:.1f} kAt/Wb'.format(R1/1000) )
print('R2 = {:.1f} kAt/Wb'.format(R2/1000) )
print('R3 = {:.1f} kAt/Wb'.format(R3/1000) )

```
```

```
In [8]:
```Rtot= R1 + R2 + R3
print('Rtot = {:.1f} kAt/Wb'.format(Rtot/1000) )

```
```

```
In [9]:
```F = phi * Rtot
print('F = {:.1f} At'.format(F) )

```
```

and the required **current is $i = \frac{\mathcal{F}}{N}$**:

```
In [10]:
```N = 500 # given in Figure P1-2
i = F/N
print('''
i = {:.1f} A
========='''.format(i))

```
```

**The flux density $B = \frac{\phi}{A}$ on the top of the core is:**

```
In [11]:
```B1 = phi / A1
print('''
B1 = {:.2f} T
==========='''.format(B1))

```
```

**The flux density $B = \frac{\phi}{A}$ at the right side of the core is:**

```
In [12]:
```B3 = phi / A3
print('''
B3 = {:.1f} T
=========='''.format(B3))

```
```