Calculate the magnetic field produced at the centre of a circle of radius 1 m around which a hydrogen nucleus moves in 1 s:

Options

A. `3.2pi xx 10^(-26)T`
B. ` 32xx10^(-26)T`
C. `32 xx 10^(-20)T`
D. `30pi xx 10^(-20) T`

Explanation

To calculate the magnetic field produced at the center of a circle of radius 1 m around which a hydrogen nucleus moves in 1 second, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the parameters**:
- Radius (r) = 1 m
- Time period (T) = 1 s
- Charge of a hydrogen nucleus (q) = Charge of a proton = \(1.6 \times 10^{-19}\) C

2. **Calculate the current (i)**:
The current can be calculated using the formula:
\[ i = \frac{q}{T} \]
Substituting the values:
\[ i = \frac{1.6 \times 10^{-19}}{1} = 1.6 \times 10^{-19} \text{ A} \]

3. **Use the formula for magnetic field (B)**:
The magnetic field at the center of a circular loop is given by:
\[ B = \frac{\mu_0 n i}{2r} \]
where:
- \(\mu_0\) (permeability of free space) = \(4\pi \times 10^{-7} \, \text{T m/A}\)
- \(n\) (number of turns) = 1 (since the hydrogen nucleus makes one complete turn)
- \(r\) = radius of the circle = 1 m

4. **Substituting the values into the formula**:
\[ B = \frac{(4\pi \times 10^{-7}) \times 1 \times (1.6 \times 10^{-19})}{2 \times 1} \]
Simplifying this:
\[ B = \frac{4\pi \times 10^{-7} \times 1.6 \times 10^{-19}}{2} \]

5. **Calculate the magnetic field**:
\[ B = \frac{4 \times 1.6 \times \pi \times 10^{-26}}{2} \]
\[ B = 3.2\pi \times 10^{-26} \text{ T} \]

6. **Final Result**:
The magnetic field at the center of the circle is:
\[ B \approx 3.2\pi \times 10^{-26} \text{ T} \]