The magnetic field at the centre of a wire loop formed by two semicircular wires of radii $R_1=2 \pi\  \mathrm{m}$ and $R_2=4 \pi\  \mathrm{m}$ carrying current $I=4 \mathrm{~A}$ as per figure given below is $\alpha \times 10^{-7} \mathrm{~T}$. The value of $\alpha$ is___________ (Centre $\mathrm{O}$ is common for all segments)

A long insulated copper wire is closely wound as a spiral of ' $N$ ' turns. The spiral has inner radius ' $a$ ' and outer radius ' $b$ '. The spiral lies in the $X-Y$ plane and a steady current ' $I$ ' flows through the wire. The $Z$-component of the magnetic field at the center of the spiral is 

A portion of a conductive wire is bent in the form of a semicircle of radius $r$ as shown below in fig. At the centre of semicircle, the magnetic induction will be

A long thin walled pipe of radius $R$ carries a current $I$ along its length. The current density is uniform over the circumference of the pipe. The magnetic field at the center of the pipe due to quarter portion of the pipe shown, is

The magnetic field at the center of current carrying circular loop is $B _{1}$. The magnetic field at a distance of $\sqrt{3}$ times radius of the given circular loop from the center on its axis is $B_{2}$. The value of $B_{1} / B_{2}$ will be.

A plastic disc of radius $R$ has a charge $q$ uniformly distributed over its surface. If the disc is rotated at an angular frequency $\omega$ about it axis, the induction at the center of the disc is :-