Which law is useful to determine the relation between current and the magnetic field produced by it?

On connecting a battery to the two corners of a diagonal of a square conductor frame of side $a$,the magnitude of the magnetic field at the centre will be:

An infinite straight current-carrying conductor is bent in such a way that a circular loop is formed on it as shown in the figure. If the radius of the loop is $R$,the magnetic field at the centre of the loop is . . . . . . .

Two identical long conducting wires $AOB$ and $COD$ are placed at a right angle to each other,with one above the other such that $O$ is their common point. The wires carry currents $I_1$ and $I_2$,respectively. Point $P$ lies at a distance $d$ from $O$ along a direction perpendicular to the plane containing the wires. The magnetic field at point $P$ will be:

An arrangement with a pair of quarter circular coils of radii $r$ and $R$ with a common centre $C$ and carrying a current $I$ is shown in the figure. The permeability of free space is $\mu_0$. The magnetic field at $C$ is

In a hydrogen atom,an electron is revolving at $6.6 \times 10^{15} \text{ rev/s}$ around the nucleus in an orbit of radius $0.47 \text{ Å}$. The magnetic field induction produced at the centre of the orbit is nearly: (in $\text{ Wb m}^{-2}$)