The magnetic field at a point $P$ situated at a perpendicular distance $R$ from a long straight wire carrying a current of $12 \ A$ is $3 \times 10^{-5} \ Wb/m^2$. The value of $R$ in $mm$ is $\left[\mu_0 = 4\pi \times 10^{-7} \ Wb/Am\right]$

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:

The magnitude of magnetic induction at the midpoint '$O$' due to the current arrangement shown in the figure is ($\mu_0$ = permeability of free space).

Consider two thin identical conducting wires covered with very thin insulating material. One of the wires is bent into a loop and produces a magnetic field $B_1$ at its centre when a current $I$ passes through it. The second wire is bent into a coil with three identical loops adjacent to each other and produces a magnetic field $B_2$ at the centre of the loops when a current $I/3$ passes through it. The ratio $B_1 : B_2$ is

Write the equation for the magnetic field due to a circular current-carrying loop at a point on the axis of the loop. Give its special cases.

$A$ current carrying circular coil of radius $R$ has a point $P$ situated on its axis at a distance $x$ from its centre $O$ of the coil. The magnetic induction at point $P$ is $\left(\frac{1}{8}\right)^{\text{th}}$ of the magnetic field at its centre $O$. The value of $x$ is