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

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

Find the magnetic induction at point $O$ in the given figure.

Find the magnetic field at point $P$ in the given diagram.

The magnetic field due to a current in a straight wire segment of length $L$ at a point on its perpendicular bisector at a distance $r$ $(r >> L)$ is:

The magnetic field due to a long straight wire carrying a current $I$ is proportional to: