Two circular coils $P$ and $Q$ are made from two identical wires of the same length. The number of turns in coils $P$ and $Q$ are $4$ and $2$,respectively. The magnetic inductions at the centers of $P$ and $Q$ are $B_P$ and $B_Q$,respectively. The ratio $\frac{B_P}{B_Q}$ is

$A$ 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 $(\mu_0 = \text{permeability of free space})$:

In the figure shown,there are two semicircles of radii $r_1$ and $r_2$ in which a current $i$ is flowing. The magnetic induction at the centre $O$ will be

Find the magnitude of the magnetic field at point $p$ due to the semi-infinite wire shown below.

Two concentric coils each of radius equal to $2\pi \text{ cm}$ are placed at right angles to each other. If $3 \text{ A}$ and $4 \text{ A}$ are the currents flowing through the two coils respectively,the magnetic induction (in $\text{Wb m}^{-2}$) at the centre of the coils will be:

$A$ current of $1\,A$ is passed through a hexagonal conducting wire of side $1\,m$. The magnetic induction at its centre $O$ in $Wb/m^2$ will be