The deflection magnetometer is most sensitive when the defiection ` theta` is

Options

A. Nearly `0^(@)`
B. Nearly `30^(@)`
C. Nearly `45^(@)`
D. Nearly `90^(@)`

Answer

To determine the angle at which a deflection magnetometer is most sensitive, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the Deflection Magnetometer**:
- A deflection magnetometer is an instrument used to measure the magnetic moment and pole strength of bar magnets. It works by measuring the angle of deflection of a magnetic needle in the presence of a magnetic field.

2. **Sensitivity of the Magnetometer**:
- The sensitivity of the deflection magnetometer is related to the angle of deflection (θ) of the magnetic needle. The sensitivity is highest when the torque acting on the needle is maximized.

3. **Torque on the Magnetic Needle**:
- The torque (τ) acting on the magnetic needle is given by the formula:
\[ τ = m \cdot B \cdot \sin(θ) \]
where:
- \( m \) is the magnetic moment of the needle,
- \( B \) is the magnetic field strength,
- \( θ \) is the angle of deflection.

4. **Maximizing the Torque**:
- To find the angle that maximizes the torque, we need to maximize the sine function. The sine function reaches its maximum value of 1 when \( θ = 90^\circ \).

5. **Conclusion**:
- Therefore, the deflection magnetometer is most sensitive when the deflection \( θ \) is \( 90^\circ \).

### Final Answer:
The deflection magnetometer is most sensitive when the deflection \( θ \) is \( 90^\circ \).

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