Find the magnetic field B at the centre of a rectangular loop of length l and width b, carrying a current i.

Explanation

To find the magnetic field \( B \) at the center of a rectangular loop of length \( l \) and width \( b \), carrying a current \( i \), we can follow these steps:

### Step 1: Understanding the Geometry
Consider a rectangular loop with vertices labeled as \( A, B, C, D \). The length of the rectangle is \( l \) and the width is \( b \). The center of the loop is the point where we want to calculate the magnetic field.

### Step 2: Magnetic Field Contribution from Each Side
The magnetic field at the center due to each side of the rectangle can be calculated using the Biot-Savart Law. The magnetic field due to a straight current-carrying wire at a distance \( r \) from the wire is given by:

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