The magnetic field at the center of a current-carrying loop of radius $0.1 \ m$ is $5\sqrt{5}$ times that at a point along its axis. The distance of this point from the center of the loop is: (in $m$)

The electric current in a circular coil of $2$ turns produces a magnetic induction $B_{1}$ at its centre. The coil is unwound and is rewound into a circular coil of $5$ turns and the same current produces a magnetic induction $B_{2}$ at its centre. The ratio of $\frac{B_{2}}{B_{1}}$ is:

If a wire of length $L$ forms a loop of radius $R$ and has $n$ turns,find the magnetic field at the center of the loop if the current flowing in the loop is $I$.

Magnetic field intensity at the centre of a coil of $50$ turns,radius $0.5\, m$ and carrying a current of $2\, A$ is:

Two long parallel wires $P$ and $Q$ are held perpendicular to the plane of the paper with a distance of $5 \; m$ between them. If $P$ and $Q$ carry currents of $2.5 \; A$ and $5 \; A$ respectively in the same direction,then the magnetic field at a point half-way between the wires is:

$A$ loop $ABCDA$,carrying current $I=12 \ A$,is placed in a plane,consists of two semi-circular segments of radius $R_1=6 \pi \ m$ and $R_2=4 \pi \ m$. The magnitude of the resultant magnetic field at center $O$ is $k \times 10^{-7} \ T$. The value of $k$ is . . . . . . . (Given $\mu_0=4 \pi \times 10^{-7} \ Tm \ A^{-1}$)