$A$ coil of $50$ turns and $4$ cm radius carries $2$ $A$ current. The magnetic field at its centre is ....... $mT$.

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

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

$A$ regular polygon of $6$ sides is formed by bending a wire of length $4 \pi \text{ m}$. If an electric current of $4 \pi \sqrt{3} \text{ A}$ is flowing through the sides of the polygon,the magnetic field at the centre of the polygon would be $x \times 10^{-7} \text{ T}$. The value of $x$ is . . . . . . .

$A$ symmetric star-shaped conducting wire loop carries a steady current $I$ as shown in the figure. The distance between the diametrically opposite vertices of the star is $4a$. The magnitude of the magnetic field at the center of the loop is:

In the following figure,the magnitude of the magnetic field at the point $P$ is: