The needle of a deflection magnetometer deflects through `45^@` from north to south when the instrument is used in Tan-A position with a magnet of length 10cm placed at a distance of 25cm. (a) Find the magnetic moment of the magnet if the earth's horizontal magnetic field is `20 muT`. (b) If the magnetometer is used in `Tan-B` position with the same magnet at the same separation from the needle, what will be the deflection?

Explanation

To solve the problem step by step, we will break it down into two parts as per the question.

### Part (a): Finding the Magnetic Moment of the Magnet

1. **Understanding the Given Data**:
- Deflection angle, θ = 45°
- Length of the magnet, 2L = 10 cm → L = 5 cm = 0.05 m
- Distance from the magnet to the compass, D = 25 cm = 0.25 m
...