$A$ straight conductor carrying current $i$ splits into two parts as shown in the figure. The radius of the circular loop is $R$. The total magnetic field at the centre $P$ of the loop is

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 $m$)

$A$ Helmholtz coil has a pair of loops,each with $N$ turns and radius $R$. They are placed coaxially at a distance $R$ apart,and the same current $I$ flows through the loops in the same direction. The magnitude of the magnetic field at $P$,the midpoint between the centers $A$ and $C$,is given by (Refer to figure):

$A$ small current element of length $d\ell$ carrying current $I$ is placed at $(1, 1, 0)$ and is carrying current in the $+z$ direction. If the magnetic field at the origin is $\vec{B}_1$ and at the point $(2, 2, 0)$ is $\vec{B}_2$,then:

Two long,straight wires carry equal currents of $10 \ A$ in opposite directions as shown in the figure. The separation between the wires is $5.0 \ cm$. The magnitude of the magnetic field at a point $P$ midway between the wires is . . . . . . $\mu T$. (Given: $\mu_0 = 4\pi \times 10^{-7} \ TmA^{-1}$)

The magnetic induction at point $O$ for the current-carrying wire shown in the figure is: