A steady current is flowing in a circular coil of radius R, made up of a thin conducting wire. The magnetic field at the centre of the loop is `B_L`. Now, a circular loop of radius `R//n` is made from the same wire without changing its length, by unfounding and refolding the loop, and the same current is passed through it. If new magnetic field at the centre of the coil is `B_C`, then the ratio `B_L//B_C` is

Options

A. `1 : n^(2)`
B. `1 : L`
C. `n : n^(2)`
D. `n : n^(1//2)`

Explanation

To solve the problem, we need to find the ratio of the magnetic fields \( \frac{B_L}{B_C} \) at the center of two circular loops made from the same wire but with different radii.

### Step-by-Step Solution:

1. **Magnetic Field at the Center of the Original Loop (B_L)**:
The magnetic field at the center of a circular loop of radius \( R \) carrying a current \( I \) is given by the formula:
\[
B_L = \frac{\mu_0 I}{2R}
...