A current $l_0$ flows through a metallic circular loop of radius $r$ as shown in the figure. Resistance of the segment $A B C$ is half that of $A D C$. Magnitude of magnetic field at the centre $O$ of the loop is :

Two infinitely long parallel conducting wires $A$ and $B$ carry currents $I$ and $2 I$, respectively, in the same direction. The wire $A$ has uniform mass per unit length $\lambda$ and lies on an insulated floor. The wire $B$ is kept fixed at a height $h$ above the floor. The minimum magnitude of $h$ so that the wire $A$ does not rise from the floor is: [ $g$ is the acceleration due to gravity and $\mu_0$ is the permeability of free space.]

A 100-turn closely wound circular coil of radius 5 cm has a magnetic field of $3.14 \times 10^{-3} \mathrm{~T}$ at its centre. The current flowing through the coil, and the magnitude of the magnetic moment of this coil are, respectively :

(Take $\mu_0=4 \pi \times 10^{-7} \mathrm{~T} \mathrm{~m} / \mathrm{A}$ )

The figure given below shows a long straight solid wire of circular cross-section of radius ' $a$ ' carrying steady current $I$. The current $I$ is uniformly distributed across its cross-section. The plot which correctly represents the variation of magnetic field $(B)$ with distance $(r)$ from the axis of the conductor in the region is :