The ratio of the magnetic field at the centre of a current-carrying coil of radius $a$ to the magnetic field at a distance $a$ from the centre of the coil along its axis is

The figure shows two semicircular loops of radii $R_1$ and $R_2$ carrying current $I$. The magnetic field at the common centre '$O$' is

In the following figure,a wire bent in the form of a regular polygon of $n$ sides is inscribed in a circle of radius $a$. The net magnetic field at the centre will be

$A$ solenoid of $1000$ turns per metre has a core with relative permeability $500$. Insulated windings of the solenoid carry an electric current of $5 \, A$. The magnetic flux density produced by the solenoid is (permeability of free space $= 4 \pi \times 10^{-7} \, H/m$)

$A$ wire of length $l$ is bent into a circular loop of radius $R$ and carries a current $I$. The magnetic field at the centre of the loop is $B$. The same wire is now bent into a double loop of equal radii. If both loops carry the same current $I$ and it is in the same direction, the magnetic field at the centre of the double loop will be

Two parallel long current-carrying wires separated by a distance $2r$ are shown in the figure. The ratio of the magnetic field at $A$ to the magnetic field produced at $C$ is $\frac{x}{7}$. The value of $x$ is $\qquad$