$A$ coil having $N$ turns is wound tightly in the form of a spiral with inner and outer radii $a$ and $b$ respectively. Find the magnetic field at the centre,when a current $I$ passes through the coil.

Given below are two statements:
Statement $I:$ Biot-Savart's law gives us the expression for the magnetic field strength of an infinitesimal current element $(Id\vec{l})$ of a current-carrying conductor only.
Statement $II:$ Biot-Savart's law is analogous to Coulomb's inverse square law of charge $q$,with the former being related to the field produced by a vector source,$Id\vec{l}$,while the latter is produced by a scalar source,$q$. In light of the above statements,choose the most appropriate answer from the options given below:

$A$ wire in the form of a square of side $a$ carries a current $i$. Then, the magnetic induction at the centre of the square is (Magnetic permeability of free space $= \mu_0$)

$A$ linear small part of wire $PQ$ is situated on the $y$-axis from $y = -a/2$ to $y = +a/2$, and a current $I$ is flowing through it. The magnetic field produced due to wire $PQ$ at the point $y = +a$ will be:

An infinitely long straight conductor is bent into the shape as shown in the figure. It carries a current of $i$ $ampere$ and the radius of the circular loop is $r$ $metre$. Then the magnetic induction at its centre $O$ will be:

The magnetic field at the center of a circular coil carrying current '$I$' for a single turn of a given length of wire is '$B$'. The same wire is bent into a circular coil having two turns. When the same current '$I$' passes through it, the value of the magnetic field becomes: