A direct current is passing through a wire. It is bent to form a coil of one turn. Now it is further bent to form a coil of two turns but at smaller radius. The ratio of the magnetic induction at the centre of this coils and at the centre of the coil of two turn is

Explanation

To solve the problem of finding the ratio of the magnetic induction at the center of a one-turn coil and a two-turn coil formed from the same wire, we can follow these steps:

### Step 1: Determine the radius of the one-turn coil
Let the length of the wire be \( L \). For a one-turn coil, the circumference is equal to the length of the wire:
\[ 2\pi R_1 = L \]
From this, we can find the radius \( R_1 \):
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