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

Two very long,straight and insulated wires are kept at a $90^o$ angle from each other in the $xy$-plane as shown in the figure. These wires carry a current of equal magnitude $I$,whose directions are shown in the figure. The net magnetic field at point $P$ will be:

When the current flowing in a circular coil is doubled and the number of turns of the coil in it is halved,the magnetic field at its centre will become

$A$ current flows through a circular coil of radius $R$. Find the distance from the center on the axis where the magnetic field is $\frac{1}{8}$th of the magnetic field at the center.

$A$ long straight wire of radius $a$ carries a steady current $I$. The current is uniformly distributed across its cross-section. The ratio of the magnetic field at $\frac{a}{2}$ and $2a$ from the axis of the wire is:

Current $i$ is passed through a circular arc as shown in the diagram. If the radius of the circle is $R$,then the magnetic flux density at the centre $P$ will be: