An arc of a circle of radius $R$ subtends an angle $\frac{\pi}{2}$ at the centre. It carries a current $i$. The magnetic field at the centre will be

$A$ long insulated copper wire is closely wound as a spiral of $N$ turns. The spiral has inner radius $a$ and outer radius $b$. The spiral lies in the $X-Y$ plane and a steady current $I$ flows through the wire. The $Z$-component of the magnetic field at the center of the spiral is

The radius of a circular coil is $R$ and it carries a current of $I$ ampere. The intensity of the magnetic field at a distance $x$ on the axis from the centre $(x >> R)$ will be:

$A$ circular coil of wire consisting of $100$ turns,each of radius $8.0 \; cm$,carries a current of $0.40 \; A$. What is the magnitude of the magnetic field $B$ at the centre of the coil?

The magnetic field $d\overrightarrow{B}$ due to a small current element $d\overrightarrow{l}$ at a distance $\overrightarrow{r}$ from an element carrying current $i$ is given by:

Two long straight wires are placed along the $x$-axis and $y$-axis. They carry currents $I_1$ and $I_2$ respectively. The equation of the locus of points with zero magnetic induction in the magnetic field produced by them is: