Which of the following gives the value of the magnetic field according to Biot-Savart's law?

To produce a uniform magnetic field directed parallel to a diameter of a cylindrical region,one can use the saddle coils illustrated in the figure. The loops are wrapped over a somewhat flattened tube. Assume the straight sections of wire are very long. The end view of the tube shows how the windings are applied. The overall current distribution is the superposition of two overlapping circular cylinders of uniformly distributed current,one toward you and one away from you. The current density $J$ is the same for each cylinder. The position of the axis of one cylinder is described by a position vector $\vec{a}$ relative to the other cylinder. The magnetic field inside the hollow tube is:

$A$ thin ring of radius $R$ meter has charge $q$ coulomb uniformly spread on it. The ring rotates about its axis with a constant frequency of $f$ revolution/s. The value of magnetic induction in $Wb/m^2$ at the center of the ring is $(\mu_0 = \text{Permeability of free space})$

$A$ steady electric current is flowing through a cylindrical wire. Which of the following statements is/are correct?
$(a)$ The electric field at the axis of the wire is zero.
$(b)$ The magnetic field at the axis of the wire is zero.
$(c)$ The electric field in the vicinity of the wire is zero.
$(d)$ The magnetic field in the vicinity of the wire is zero.

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

An electric current passes through a long straight wire. At a distance $5 \ cm$ from the wire,the magnetic field is $B$. The magnetic field at $20 \ cm$ from the wire would be: