A circular coil of N turns and radius R carries a current I. It is unwound and rewound to make another coil of radius `R//2.` Current I remaining the same. Calculate the ratio of the magnetic moments of the new coil and the original coil.

Explanation

To solve the problem, we will calculate the magnetic moments of both the original coil and the new coil, and then find their ratio.

### Step-by-Step Solution:

1. **Identify the parameters of the original coil:**
- Number of turns: \( N_1 = N \)
- Radius: \( R \)
- Current: \( I \)
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