Two magnets of magnetic moments `4Am^(2) and 3Am^(2)` are joined to form a cross `(+)`, then the magnetic moment of the combination is

Options

A. `4Am^(2)`
B. `1Am^(2)`
C. `7Am^(2)`
D. `5Am^(2)`

Answer

To solve the problem of finding the magnetic moment of two magnets joined to form a cross, we can follow these steps:

### Step-by-Step Solution:

1. **Identify the Magnetic Moments**:
We have two magnets with magnetic moments:
- \( m_1 = 4 \, \text{A m}^2 \)
- \( m_2 = 3 \, \text{A m}^2 \)

2. **Understand the Configuration**:
The magnets are arranged in a cross formation, which means they are oriented at right angles (90 degrees) to each other. This implies that the magnetic moments \( m_1 \) and \( m_2 \) are perpendicular.

3. **Use the Formula for Resultant Magnetic Moment**:
When two magnetic moments are perpendicular, the resultant magnetic moment \( m_{\text{net}} \) can be calculated using the Pythagorean theorem:
\[ m_{\text{net}} = \sqrt{m_1^2 + m_2^2} \]

4. **Substitute the Values**:
Now, substituting the values of \( m_1 \) and \( m_2 \):
\[ m_{\text{net}} = \sqrt{(4 \, \text{A m}^2)^2 + (3 \, \text{A m}^2)^2} \]
\[ = \sqrt{16 + 9} \]
\[ = \sqrt{25} \]

5. **Calculate the Result**:
\[ m_{\text{net}} = 5 \, \text{A m}^2 \]

6. **Conclusion**:
The magnetic moment of the combination is \( 5 \, \text{A m}^2 \).

### Final Answer:
The magnetic moment of the combination is \( 5 \, \text{A m}^2 \).

---