$A$ circular coil carrying current has radius $R$. The distance from the centre of the coil on the axis where the magnetic induction will be $\frac{1}{27}$th of its value at the centre of the coil is:

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

The magnetic induction due to an infinitely long straight wire carrying a current $i$ at a distance $r$ from the wire is given by:

$A$ wire carrying current $I$ has the shape as shown in the adjoining figure. The linear parts of the wire are very long and parallel to the $X$-axis,while the semicircular portion of radius $R$ lies in the $Y-Z$ plane. The magnetic field at point $O$ is:

Two long straight wires are placed along the $x$-axis and $y$-axis. They carry currents $I_1$ and $I_2$ respectively. The equation of the locus of points with zero magnetic induction in the magnetic field produced by them is:

Two long straight wires,each carrying a current $I$ in opposite directions,are separated by a distance $R$. The magnetic induction at a point midway between the wires is