$A$ current $i$ flows through a square loop of side $a$. What is the magnetic field at its center?

The magnetic field $d\overrightarrow{B}$ due to a small current element $d\overrightarrow{l}$ at a distance $\overrightarrow{r}$ from an element carrying current $i$ is given by:

$A$ long straight wire carries a current of $35\, A$. What is the magnitude of the magnetic field $B$ at a point $20\, cm$ from the wire?

The magnetic field at the centre $O$ of a wire loop formed by two semicircular wires of radii $R_1=2 \pi \text{ m}$ and $R_2=4 \pi \text{ m}$ carrying current $I=4 \text{ A}$ as per the figure given below is $\alpha \times 10^{-7} \text{ T}$. The value of $\alpha$ is . . . . . . . (Centre $O$ is common for all segments)

An element $\Delta l = \Delta x \hat{i}$ is placed at the origin and carries a large current $I = 10 \; A$ (Figure). What is the magnetic field on the $y$-axis at a distance of $0.5 \; m$? Given $\Delta x = 1 \; cm$.

$A$ current $I$ flows around a closed path in the horizontal plane as shown in the figure. The path consists of eight arcs with alternating radii $r$ and $2r$. Each segment of arc subtends an equal angle at the common centre $P$. The magnetic field produced by the current path at point $P$ is