Two identical current carrying coils of radius 10 cm each are placed coaxially` 0.5` m apart. Find the magnetic fields at the centre of each coil if a current of `0.5` A is passed through each of them in opposite directions. Assume that each coil is made of a single turn.

Explanation

To solve the problem of finding the magnetic fields at the center of two identical current-carrying coils placed coaxially and 0.5 m apart, we will follow these steps:

### Step 1: Understand the Setup
We have two identical coils, each with a radius of \( r = 10 \, \text{cm} = 0.1 \, \text{m} \), separated by a distance \( d = 0.5 \, \text{m} \). A current \( I = 0.5 \, \text{A} \) flows through each coil in opposite directions.

### Step 2: Magnetic Field Due to a Single Coil
The magnetic field \( B \) at the center of a single circular coil carrying current \( I \) is given by the formula:
\[
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