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

$B_{X}$ and $B_{Y}$ are the magnetic fields at the centre of two coils $X$ and $Y$ respectively,each carrying equal current. If coil $X$ has $200$ turns and $20 \ cm$ radius and coil $Y$ has $400$ turns and $20 \ cm$ radius,the ratio of $B_{X}$ and $B_{Y}$ is:

$A$ thin charged rod is bent into the shape of a small circle of radius $R$, the charge per unit length of the rod being $\lambda$. The circle is rotated about its axis with a time period $T$, and it is found that the magnetic field at a distance $d$ away $(d >> R)$ from the center and on the axis varies as $\frac{R^{m}}{d^{n}}$. The values of $m$ and $n$ respectively are:

Two infinitely long parallel wires carry equal current in the same direction. The magnetic field at a midpoint between the two wires is

$A$ steady current $I$ flows through a wire loop $PQR$ having the shape of a right-angled triangle with $PQ = 3x$, $PR = 4x$, and $QR = 5x$. If the magnitude of the magnetic field at $P$ due to this loop is $k \left( \frac{\mu_0 I}{48 \pi x} \right)$, find the value of $k$.

The magnetic field induction at the centre of a circular coil of radius $5 \,cm$ carrying a current of $0.9 \,A$ is (in $SI$ units) (where $\varepsilon_0$ is the absolute permittivity of air in $SI$ units, and the velocity of light $c = 3 \times 10^8 \,ms^{-1}$):