$A$ circular loop of radius $r$ is carrying current $I \ A$. The ratio of the magnetic field at the centre of the circular loop to the magnetic field at a distance $r$ from the centre of the loop on its axis is:

The magnetic induction at the centre $O$ in the figure shown is

$A$ particle carrying a charge equal to $100$ times the charge on an electron is rotating one rotation per second in a circular path of radius $0.8 \ m$. The value of magnetic field produced at the centre will be $(\mu_0 = \text{permeability of vacuum})$

The ratio of the magnetic field at the centre of a current-carrying coil of radius $r$ to the magnetic field at a distance $r$ from the centre of the coil on its axis is $\sqrt{x}: 1$. The value of $x$ 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

Two infinitely long wires are placed at $(1 \text{ cm}, 1 \text{ cm})$ and $(1 \text{ cm}, -1 \text{ cm})$ with $1 \text{ A}$ current in each and in the same directions perpendicular to the $xy$-plane. Let the magnetic field due to these current-carrying wires at the origin be $B$. If $B_0$ is the magnitude of the field if only one of them was present,then $\frac{|B|}{B_0}$ is