A wire of length L is bent around in the form of a coil having N turns of same radius . If a steady current I flows through it in a clockwise direction, find the magnitude and direction of the magnetic field produced at its centre.

Explanation

To find the magnitude and direction of the magnetic field produced at the center of a coil formed by bending a wire of length \( L \) with \( N \) turns and carrying a steady current \( I \), we can follow these steps:

### Step 1: Determine the Radius of the Coil
The length of the wire \( L \) is equal to the circumference of the coil multiplied by the number of turns \( N \). The circumference of a circle is given by \( 2\pi r \), where \( r \) is the radius. Therefore, we can express this relationship as:
\[ L = N \cdot 2\pi r \]
From this, we can solve for the radius \( r \):
...