The magnetic field at a distance d from a short bar magnet in longitudinal and transverse positions are in the ratio.

Explanation

To solve the problem of finding the ratio of the magnetic fields at a distance \( d \) from a short bar magnet in longitudinal and transverse positions, we can follow these steps:

### Step 1: Understand the Magnetic Field Formulas
For a short bar magnet, the magnetic field at a distance \( d \) can be expressed in two different configurations:
- **Longitudinal Position**: The magnetic field \( B_1 \) is given by the formula:
\[ B_1 = \frac{\mu_0 \cdot 2m}{4\pi d^3} \]
- **Transverse Position**: The magnetic field \( B_2 \) is given by the formula:
\[ B_2 = \frac{\mu_0 \cdot m}{4\pi d^3} \]

### Step 2: Set Up the Ratio
We need to find the ratio \( \frac{B_1}{B_2} \):
\[ \frac{B_1}{B_2} = \frac{\frac{\mu_0 \cdot 2m}{4\pi d^3}}{\frac{\mu_0 \cdot m}{4\pi d^3}} \]

### Step 3: Simplify the Ratio
When we simplify the ratio, we can cancel out the common terms:
\[ \frac{B_1}{B_2} = \frac{2m}{m} = 2 \]

### Step 4: Final Ratio
Thus, the ratio of the magnetic fields in the longitudinal and transverse positions is:
\[ \frac{B_1}{B_2} = 2:1 \]

### Conclusion
The magnetic field at a distance \( d \) from a short bar magnet in longitudinal and transverse positions is in the ratio \( 2:1 \).

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