A short bar magnet X of magnetic moment M is placed horizontally with its magnetic moment directed from west to east. Another short magnet Y of magnetic moment `(2)/(sqrt3) M` is placed with its magnetic axis perpendicular to X and magnetic moment directed from north to south. Calculate the inclination of resultant magnetic field with the axis of X at a distance r from its prolonged axis.

Explanation

To solve the problem, we need to calculate the inclination of the resultant magnetic field with the axis of magnet X at a distance \( r \) from its prolonged axis. We will proceed step by step.

### Step 1: Understanding the Magnetic Fields
- **Magnet X** has a magnetic moment \( M \) directed from west to east.
- **Magnet Y** has a magnetic moment \( \frac{2}{\sqrt{3}} M \) directed from north to south, and it is placed perpendicular to Magnet X.

### Step 2: Calculate the Magnetic Field due to Magnet X
The magnetic field \( B_1 \) at a distance \( r \) along the axis of a bar magnet is given by the formula:
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