A ring of mean radius 15 cm has 3500 turns of wire wound on a ferromagnetic core of relative permeability 800. The magnetic field in the core for a magnetising current of 1.2 A is

Options

A. 2.48T
B. 3.48T
C. 4.48T
D. 5.48T

Explanation

To find the magnetic field \( B \) in the ferromagnetic core of the ring, we can use the formula:

\[ B = \mu n I \]

where:
- \( \mu \) is the permeability of the material,
- \( n \) is the number of turns per unit length,
- \( I \) is the magnetizing current.

### Step-by-step Solution:

1. **Calculate the Length of the Ring:**
The length \( L \) of the ring can be calculated using the formula for the circumference of a circle:
\[ L = 2\pi R \]
Given that the mean radius \( R = 0.15 \, \text{m} \):
\[ L = 2\pi \times 0.15 \approx 0.942 \, \text{m} \]

2. **Calculate the Number of Turns per Unit Length \( n \):**
The number of turns per unit length \( n \) is given by:
\[ n = \frac{N}{L} \]
where \( N = 3500 \) turns. Thus:
\[ n = \frac{3500}{0.942} \approx 3712.8 \, \text{turns/m} \]

3. **Calculate the Permeability \( \mu \):**
The permeability \( \mu \) can be calculated using the relative permeability \( \mu_r \):
\[ \mu = \mu_r \mu_0 \]
where \( \mu_0 = 4\pi \times 10^{-7} \, \text{T m/A} \) and \( \mu_r = 800 \):
\[ \mu = 800 \times (4\pi \times 10^{-7}) \approx 3.2 \times 10^{-4} \, \text{T m/A} \]

4. **Substitute Values into the Magnetic Field Formula:**
Now substituting the values into the magnetic field formula:
\[ B = \mu n I \]
where \( I = 1.2 \, \text{A} \):
\[ B = (3.2 \times 10^{-4}) \times (3712.8) \times (1.2) \]

5. **Calculate \( B \):**
Performing the multiplication:
\[ B \approx 3.2 \times 10^{-4} \times 3712.8 \times 1.2 \approx 0.00143 \, \text{T} \approx 1.43 \, \text{mT} \]

### Final Result:
Thus, the magnetic field \( B \) in the core is approximately \( 1.43 \, \text{mT} \).