$A$ vertical straight conductor carries a current vertically upwards. $A$ point $P$ lies to the east of it at a small distance and another point $Q$ lies to the west at the same distance. The magnetic field at $P$ is

How can we determine the direction of the magnetic field using the Biot-Savart law?

Apply the Biot-Savart law to find the magnetic field due to a circular current-carrying loop at a point on the axis of the loop.

$A$ long straight wire carries a current of $\pi \, A$. The magnetic field due to it will be $5 \times 10^{-5} \, Wb/m^2$ at what distance from the wire? $[\mu_0 = \text{permeability of free space}]$

As shown in the figure,two infinitely long,identical wires are bent by $90^{\circ}$ and placed in such a way that the segments $LP$ and $QM$ are along the $x-$ axis,while segments $PS$ and $QN$ are parallel to the $y-$ axis. If $OP = OQ = 4\, cm$,the magnitude of the magnetic field at $O$ is $10^{-4}\, T$,and the two wires carry equal current $i$ (see figure),find the magnitude of the current in each wire and the direction of the magnetic field at $O$. $(\mu_0 = 4\pi \times 10^{-7}\, NA^{-2})$

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: