In a hydrogen atom,an electron moves in a circular orbit of radius $5.2 \times 10^{-11} \, m$ and produces a magnetic induction of $12.56 \, T$ at its nucleus. The current produced by the motion of the electron will be (Given $\mu_0 = 4\pi \times 10^{-7} \, Wb/A \cdot m$)

The magnetic field at point $P$ is:

Two wires $A$ and $B$ are of lengths $40 \ cm$ and $30 \ cm$. $A$ is bent into a circle of radius $r$ and $B$ into an arc of radius $r$. $A$ current $i_1$ is passed through $A$ and $i_2$ through $B$. To have the same magnetic inductions at the centre,the ratio of $i_1: i_2$ is

Charge $q$ is uniformly spread on a thin ring of radius $R.$ The ring rotates about its axis with a uniform frequency $f \ Hz.$ The magnitude of magnetic induction at the center of the ring is

$A$ wire of length $l$ is bent into a circular coil of one turn of radius $R_1$. Another wire of the same material and same area of cross-section and same length is bent into a circular coil of two turns of radius $R_2$. When the same current flows through the two coils,the ratio of magnetic induction at the centres of the two coils is

$A$ circular coil of radius $R$ is carrying a current $I_{1}$ in an anticlockwise sense. $A$ long straight wire is carrying a current $I_{2}$ in the negative direction of the $x$-axis. Both are placed in the same plane and the distance between the centre of the coil and the straight wire is $d$. The magnetic field at the centre of the coil will be zero for the value of $d$ equal to: