A wire of length l is bent in the form of an equilateral triangle and carries an electric current i. (a) Find the magnetic field B at the centre. (b) If the wire is bent in the form of a square, what would be the value of B at the centre?

Explanation

To solve the problem, we will break it down into two parts: (a) finding the magnetic field at the center of an equilateral triangle and (b) finding the magnetic field at the center of a square.

### Part (a): Magnetic Field at the Center of an Equilateral Triangle

1. **Understanding the Geometry**:
- An equilateral triangle has three equal sides. Let the length of each side be \( \frac{L}{3} \) since the total length of the wire is \( L \).
- The angles of the equilateral triangle are \( 60^\circ \).

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