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 $............$

As shown in the figure,two infinitely long,identical wires are bent by $90^{\circ}$ and placed in such a way that the segments $LP$ and $QM$ are along the $x-$ axis,while segments $PS$ and $QN$ are parallel to the $y-$ axis. If $OP = OQ = 4\, cm$,the magnitude of the magnetic field at $O$ is $10^{-4}\, T$,and the two wires carry equal current $i$ (see figure),find the magnitude of the current in each wire and the direction of the magnetic field at $O$. $(\mu_0 = 4\pi \times 10^{-7}\, NA^{-2})$

If $B_1$ is the magnetic field induction at a point on the axis of a circular coil of radius $R$ situated at a distance $R \sqrt{3}$ and $B_2$ is the magnetic field at the centre of the coil,then the ratio of $\frac{B_1}{B_2}$ is equal to

The magnetic field at the centre of a current-carrying circular coil of radius $R$ is $B_c$ and the magnetic field at a point on its axis at a distance $R$ from its centre is $B_a$. The value of $\frac{B_c}{B_a}$ is

The magnetic field on the axis of a circular loop of radius $R = 100\,cm$ carrying current $I = \sqrt{2}\,A$,at a point $x = 1\,m$ away from the centre of the loop is given by:

Two concentric coils of $20$ turns each are placed in the same plane. Their radii are $30 \text{ cm}$ and $60 \text{ cm}$,and they carry $0.4 \text{ A}$ and $0.6 \text{ A}$ currents,respectively,in opposite directions. The magnetic induction at the centre in tesla is ....... .