Two concentric circular coils $A$ and $B$ having radii $20 \ cm$ and $10 \ cm$ respectively lie in the same plane. The current in coil $A$ is $0.5 \ A$ in anticlockwise direction. The current in coil $B$,so that net magnetic field at the common centre is zero,is

$A$ thin ring of radius $R$ meter has charge $q$ coulomb uniformly spread on it. The ring rotates about its axis with a constant frequency of $f$ revolution/s. The value of magnetic induction in $Wb/m^2$ at the center of the ring is $(\mu_0 = \text{Permeability of free space})$

$A$ current of $i$ ampere is flowing through each of the bent wires as shown. Find the magnitude of the magnetic field at $O$.

The resistances of three parts of a circular loop are as shown in the figure. The magnetic field at the centre $O$ 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 $(\mu_0 = \text{permeability of free space})$:

An infinitely long straight conductor is bent into the shape as shown below. It carries a current of $I$ ampere and the radius of the circular loop is $R$ metre. Then, the magnitude of magnetic induction at the centre of the circular loop is