(a) Using Biot-Savart's law, derive the expression for the magnetic field in the vector form at a point on the axis of a circular current loop.
(b) What does a toroid consist of? Find out the expression for the magnetic field inside a toroid for N turns of the coil having the average radius r and carrying a current I. Show the magnetic field in the open space inside and exterior to the toroid is Zero.

Explanation

### Solution:

**(a) Deriving the expression for the magnetic field at a point on the axis of a circular current loop using Biot-Savart's Law:**

1. **Understanding the Setup:**
- Consider a circular current loop of radius \( r \) carrying a current \( I \).
- We want to find the magnetic field \( \mathbf{B} \) at a point \( P \) located on the axis of the loop at a distance \( d \) from the center of the loop.

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