Two magnets, each of magnetic miment 'M' are placed so as to form a cross at right angles to each other. The magnetic moment of the system will be

Options

A. 2 M
B. `M sqrt(2)`
C. `M/2`
D. `M/(sqrt2)`

Answer

To solve the problem of finding the magnetic moment of the system formed by two magnets placed at right angles to each other, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Configuration**:
- We have two magnets, each with a magnetic moment \( M \).
- They are arranged such that they are perpendicular to each other, forming a cross.

2. **Using the Formula for Resultant Magnetic Moment**:
- The formula for the resultant magnetic moment \( M_r \) of two magnetic moments \( M_1 \) and \( M_2 \) that are at an angle \( \theta \) to each other is given by:
\[ M_r = \sqrt{M_1^2 + M_2^2 + 2 M_1 M_2 \cos \theta} \]

3. **Substituting the Values**:
- In our case, both magnetic moments are equal, so \( M_1 = M \) and \( M_2 = M \).
- The angle \( \theta \) between them is \( 90^\circ \), for which \( \cos 90^\circ = 0 \).
- Substituting these values into the formula gives:
\[ M_r = \sqrt{M^2 + M^2 + 2 \cdot M \cdot M \cdot \cos 90^\circ} \]
\[ M_r = \sqrt{M^2 + M^2 + 0} \]
\[ M_r = \sqrt{2M^2} \]

4. **Simplifying the Expression**:
- Simplifying \( \sqrt{2M^2} \) results in:
\[ M_r = \sqrt{2} \cdot M \]

5. **Final Result**:
- Therefore, the magnetic moment of the system is:
\[ M_r = M\sqrt{2} \]

### Conclusion:
The magnetic moment of the system formed by the two magnets placed at right angles to each other is \( M\sqrt{2} \).