The magnet induction at a point 1 Ã… away from a proton measured along its axis of spin is (magnetic moment of the proton is `1.4xx10^(-26)"A m"^(2)`)

Options

A. 0.28 mT
B. 28 mT
C. 0.028 mT
D. 2.8 mT

Explanation

To solve the problem of finding the magnetic induction at a point 1 Å away from a proton measured along its axis of spin, we can follow these steps:

### Step-by-Step Solution:

1. **Identify Given Quantities:**
- The magnetic moment of the proton, \( m = 1.4 \times 10^{-26} \, \text{A m}^2 \).
- The distance from the proton, \( r = 1 \, \text{Å} = 1 \times 10^{-10} \, \text{m} \).

2. **Use the Formula for Magnetic Induction:**
- When the distance \( r \) is very small compared to the length of the magnet (in this case, the proton), the magnetic induction \( B \) at a distance \( r \) along the axis of the magnetic moment can be calculated using the formula:
\[ B = \frac{\mu_0}{4\pi} \cdot \frac{2m}{r^3} \]
- Here, \( \mu_0 \) (the permeability of free space) is approximately \( 4\pi \times 10^{-7} \, \text{T m/A} \).

3. **Substitute the Values into the Formula:**
- Substitute \( \mu_0 \), \( m \), and \( r \) into the equation:
\[ B = \frac{4\pi \times 10^{-7}}{4\pi} \cdot \frac{2 \times 1.4 \times 10^{-26}}{(1 \times 10^{-10})^3} \]
- The \( 4\pi \) cancels out:
\[ B = 10^{-7} \cdot \frac{2 \times 1.4 \times 10^{-26}}{(1 \times 10^{-30})} \]

4. **Calculate \( r^3 \):**
- Calculate \( (1 \times 10^{-10})^3 = 1 \times 10^{-30} \).

5. **Calculate the Magnetic Induction:**
- Now plug in the values:
\[ B = 10^{-7} \cdot \frac{2 \times 1.4 \times 10^{-26}}{1 \times 10^{-30}} \]
\[ B = 10^{-7} \cdot 2.8 \times 10^{4} \, \text{T} \]
\[ B = 2.8 \times 10^{-3} \, \text{T} \]

6. **Convert to Millitesla:**
- Since \( 1 \, \text{T} = 1000 \, \text{mT} \):
\[ B = 2.8 \, \text{mT} \]

7. **Final Result:**
- The magnetic induction at a point 1 Å away from the proton is \( 2.8 \, \text{mT} \).

### Conclusion:
The correct answer is \( 2.8 \, \text{mT} \).