Calculate the intensity of the magnetic field at the centre of coil if the coil counts 35 turns, radius 1 m moving with a current of 7.5 A?

Options

A. 12 T
B. 300 T
C. `8.2 xx 10 ^(-4) T`
D. 554 T

Explanation

To calculate the intensity of the magnetic field at the center of a coil, we can use the formula:

\[ B = \frac{\mu_0 n I}{2r} \]

Where:
- \( B \) = magnetic field intensity at the center of the coil (in Tesla)
- \( \mu_0 \) = permeability of free space = \( 4\pi \times 10^{-7} \, \text{T m/A} \)
- \( n \) = number of turns of the coil
- \( I \) = current flowing through the coil (in Amperes)
- \( r \) = radius of the coil (in meters)

### Step-by-Step Solution:

1. **Identify the given values:**
- Number of turns, \( n = 35 \)
- Radius, \( r = 1 \, \text{m} \)
- Current, \( I = 7.5 \, \text{A} \)

2. **Substitute the values into the formula:**
\[ B = \frac{4\pi \times 10^{-7} \times 35 \times 7.5}{2 \times 1} \]

3. **Calculate the numerator:**
- First, calculate \( 4\pi \):
\[ 4\pi \approx 4 \times 3.14 = 12.56 \]
- Now calculate \( 12.56 \times 35 \times 7.5 \):
\[ 12.56 \times 35 = 439.6 \]
\[ 439.6 \times 7.5 = 3297 \]

4. **Calculate the entire expression:**
\[ B = \frac{3297 \times 10^{-7}}{2} \]
\[ B = 1648.5 \times 10^{-7} \, \text{T} \]

5. **Final result:**
\[ B = 1.6485 \times 10^{-4} \, \text{T} \, \text{or} \, 1648.5 \times 10^{-7} \, \text{T} \]

### Conclusion:
The intensity of the magnetic field at the center of the coil is \( 1648.5 \times 10^{-7} \, \text{T} \).