At what distance on the axis, from the centre of a circular current carrying coil of radius $r$, the magnetic field becomes $1 / 8$ th of the magnetic field at centre?

Two identical coils of radius $R$ and number of turns $N$ are placed perpendicular to each others in such a way that they have common centre. The current through them are $I$ and $I\sqrt 3$ . The resultant intensity of magnetic field at the centre of the coil will be  (in $weber/m^2)2$

The magnetic field at the centre of a circular coil of radius $r$ carrying current $I$ is ${B_1}$. The field at the centre of another coil of radius $2 r$ carrying same current $I$ is ${B_2}$. The ratio $\frac{{{B_1}}}{{{B_2}}}$ is

In a hydrogen atom, an electron moves in a circular orbit of radius $5.2 \times {10^{ - 11}}\,m$ and produces a magnetic induction of $12.56\, T$ at its nucleus. The current produced by the motion of the electron will be (Given ${\mu _0} = 4\pi \times {10^{ - 7}}\,Wb/A - m)$

A current $I$ flows in an infinitely long wire with cross-section in the form of a semicircular ring of radius $R$ . The magnitude of the magnetic induction along its axis is

A straight conductor carrying current $i$ splits into two parts as shown in the figure. The radius of the circular loop is $R$. The total magnetic field at the centre $P$ of the loop is