A short bar magnet has magnetic moment.
Calculate the magnetic field intensity at a distance of 0.2m from its centre on axial line?

Options

A. `1.5 xx 10^(-4) T`
B. `1.25 xx 10^(-4) T`
C. `1.5 xx 10^(-3) T`
D. `1.25 xx 10^(-3)T`

Explanation

To calculate the magnetic field intensity (B) at a distance of 0.2 m from the center of a short bar magnet on its axial line, we can use the formula:

\[ B = \frac{\mu_0}{4\pi} \cdot \frac{2M}{r^3} \]

where:
- \( B \) is the magnetic field intensity,
- \( \mu_0 \) is the permeability of free space, which is approximately \( 10^{-7} \, \text{T m/A} \),
- \( M \) is the magnetic moment of the magnet,
- \( r \) is the distance from the center of the magnet.

### Step-by-Step Solution:

1. **Identify the Given Values:**
- Magnetic moment \( M = 50 \, \text{A m}^2 \)
- Distance \( r = 0.2 \, \text{m} \)

2. **Substitute the Values into the Formula:**
\[ B = \frac{10^{-7}}{4\pi} \cdot \frac{2 \times 50}{(0.2)^3} \]

3. **Calculate \( (0.2)^3 \):**
\[ (0.2)^3 = 0.008 \, \text{m}^3 \]

4. **Calculate \( \frac{2 \times 50}{(0.2)^3} \):**
\[ \frac{2 \times 50}{0.008} = \frac{100}{0.008} = 12500 \]

5. **Substitute Back into the Formula:**
\[ B = \frac{10^{-7}}{4\pi} \cdot 12500 \]

6. **Calculate \( \frac{10^{-7}}{4\pi} \):**
- Using \( \pi \approx 3.14 \):
\[ 4\pi \approx 12.56 \implies \frac{10^{-7}}{12.56} \approx 7.96 \times 10^{-9} \, \text{T m/A} \]

7. **Final Calculation of B:**
\[ B \approx 7.96 \times 10^{-9} \cdot 12500 \approx 9.95 \times 10^{-5} \, \text{T} \]

8. **Convert to Tesla:**
\[ B \approx 1.25 \times 10^{-3} \, \text{T} \]

### Final Answer:
The magnetic field intensity at a distance of 0.2 m from the center of the short bar magnet on its axial line is approximately \( 1.25 \times 10^{-3} \, \text{T} \).