The magnetic field due to a current-carrying square loop of side $a$ at a point located symmetrically at a distance of $a/2$ from its centre (as shown in the figure) is:

The magnitude of the magnetic field at $O$ due to a current-carrying loop as shown in the figure is, where $O$ is the center of two circular portions with radii $1 \, cm$ and $2 \, cm$ respectively. (Take the value of current $I = \frac{1.2}{\pi} \, A$)

$A$ thin ring of $10 \, cm$ radius carries a uniformly distributed charge. The ring rotates at a constant angular speed of $40 \pi \, rad \, s^{-1}$ about its axis,perpendicular to its plane. If the magnetic field at its centre is $3.8 \times 10^{-9} \, T$,then the charge carried by the ring is close to $\left( \mu_0 = 4 \pi \times 10^{-7} \, N/A^2 \right)$.

Shown in the figure is a conductor carrying a current $I$. The magnetic field intensity at the point $O$ (common centre of all the three arcs) is

The magnetic field at point $P$ is:

Two concentric coplanar circular loops of radii $r_1$ and $r_2$ carry currents $i_1$ and $i_2$ in opposite directions (one clockwise and the other anticlockwise). The magnetic induction at the center of the loops is half that due to $i_1$ alone at the center. If $r_2 = 2r_1$,find the value of $\frac{i_2}{i_1}$.