Two infinitely long wires are placed at $(1 \text{ cm}, 1 \text{ cm})$ and $(1 \text{ cm}, -1 \text{ cm})$ with $1 \text{ A}$ current in each and in the same directions perpendicular to the $xy$-plane. Let the magnetic field due to these current-carrying wires at the origin be $B$. If $B_0$ is the magnitude of the field if only one of them was present,then $\frac{|B|}{B_0}$ is

$A$ and $B$ are two concentric circular loops carrying currents $i_1$ and $i_2$ as shown in the figure. If the ratio of their radii is $1:2$ and the ratio of the magnetic flux densities at the centre $O$ due to $A$ and $B$ is $1:3$,then the value of $\frac{i_1}{i_2}$ will be

Two long parallel wires carrying currents $8 \text{ A}$ and $15 \text{ A}$ in opposite directions are placed at a distance of $7 \text{ cm}$ from each other. $A$ point $P$ is equidistant from both the wires such that the lines joining the point $P$ to the wires are perpendicular to each other. The magnetic field at $P$ is $X \times 10^{-6} \text{ T}$. Find $X$. (Given: $\sqrt{2} = 1.4, \mu_0 = 4\pi \times 10^{-7} \text{ SI unit}$)

$A$ long curved conductor carries a current $I$. $A$ small current element of length $dl$ on the wire induces a magnetic field at a point away from the current element. If the position vector between the current element and the point is $\vec{r}$, making an angle $\theta$ with the current element, then the induced magnetic field density $d\vec{B}$ at the point is $(\mu_0 = \text{permeability of free space})$:

$A$ wire carrying current $I$ has the shape as shown in the adjoining figure. The linear parts of the wire are very long and parallel to the $X$-axis,while the semicircular portion of radius $R$ lies in the $Y-Z$ plane. The magnetic field at point $O$ is:

Write the formula for the magnetic field at a perpendicular distance $r$ from a finite current-carrying wire.