Magnetic fields at two points on the axis of a circular coil at a distance of $0.05\, m$ and $0.2\, m$ from the centre are in the ratio $8: 1$. The radius of the coil is .......... $m$.

$A$ steady current flows in a long wire. It is bent into a circular loop of one turn and the magnetic field at the centre of the coil is $B$. If the same wire is bent into a circular loop of $n$ turns, the magnetic field at the centre of the coil is

What is the ratio of the magnetic field at point $O$ in the given figures?

$A$ wire bent in the shape of a regular $n$-polygonal loop carries a steady current $I$. Let $l$ be the perpendicular distance of a given segment and $R$ be the distance of a vertex from the centre of the loop. The magnitude of the magnetic field at the centre of the loop is given by

$A$ thin circular frame of radius $a$ is made of insulating material. $A$ square loop is constructed within it. If the loop carries current $I$,then the magnetic induction at the geometrical centre $O$ will be:

$A$ circular coil is in the $y-z$ plane with its centre at the origin. The coil carries a constant current. Assuming the direction of the magnetic field at $x = -25 \, cm$ to be the positive direction of the magnetic field,which of the following graphs shows the variation of the magnetic field along the $x-$ axis?