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 .......... $m$.

$A$ $10 \ A$ current is passing through a very long wire of radius $5 \ cm$. The magnetic field at a distance of $2 \ cm$ inside from its curved surface is . . . . . . $\times 10^{-5} \ T$.

$A$ circular arc of radius $r$ carrying current $I$ subtends an angle $\frac{\pi}{16}$ at its centre. The radius of the metal wire is uniform. The magnetic induction at the centre of the circular arc is [where $\mu_0$ is the permeability of free space].

$A$ current-carrying loop $ABCD$ has two circular arcs $AD$ and $BC$ with radii $1 \text{ cm}$ and $2 \text{ cm}$ respectively,as shown in the figure. The two arcs $AD$ and $BC$ subtend a common angle of $30^{\circ}$ at the centre $O$. If the current flowing in the loop is $\frac{1.2}{\pi} \text{ A}$,then the magnitude of the net magnetic field at $O$ is (Given $\mu_0 = 4\pi \times 10^{-7} \text{ T m/A}$): (in $\mu \text{T}$)

Two long straight wires,each carrying a current $I$ in opposite directions,are separated by a distance $R$. The magnetic induction at a point midway between the wires is

The magnetic field intensity at the centre of a circular wire of radius $0.1 \,m$ carrying a current of $0.2 \,A$ is: