Using Biot-Savart's law, derive an expression for the magnetic field at the center of a circular coil carrying current

Give an expression for magnetic field on the axis of a circular current loop. (Expression only).

Derive an expression for the mutual induction between pair of coil.

Using this law, derive an expression for electric field due to thin uniformly charged shell.

Biot - Savart's law relates current with the magnetic field produced by it. Using the law derive an expression for intensity of magnetic field at a point at distance x from the center and on the axis of a circular current loop