Two identical long current-carrying wires are bent into the shapes shown in the following figures. If the magnitudes of the magnetic fields at the centers $P$ and $Q$ of the semicircular arcs are $B_1$ and $B_2$ respectively, then the ratio $\frac{B_1}{B_2}$ is . . . . . . .

$A$ current $I$ flows around a closed path in the horizontal plane as shown in the figure. The path consists of eight arcs with alternating radii $r$ and $2r$. Each segment of arc subtends an equal angle at the common centre $P$. The magnetic field produced by the current path at point $P$ is

The radius of a circular coil is $R$ and it carries a current of $I$ ampere. The intensity of the magnetic field at a distance $x$ on the axis from the centre $(x >> R)$ will be:

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

The magnetic field due to a current-carrying circular loop of radius $3 \ cm$ at a point on the axis at a distance of $4 \ cm$ from the centre is $54 \ \mu T$. What will be its value at the centre of the loop? (in $\mu T$)

Two circular coils $X$ (smaller) and $Y$ (bigger), each having a single turn, carry equal currents in the same direction and subtend the same angle at point '$O$' along the axis of the coil. The distances of the centers of coil to point '$O$' are $d$ and $(d/2)$ for coil $Y$ and $X$ respectively. The radii of coils $Y$ and $X$ are $(2r)$ and $(r)$ respectively. The magnetic induction due to the bigger coil at point '$O$' is $B_y$ and that due to smaller coil $X$ at point '$O$' is $B_x$. $(d \gg r)$ The relation between $B_x$ and $B_y$ is