$A$ current $I$ flows in a circular arc of radius $r$ subtending an angle $\theta$ at the centre $O$ as shown in the figure. Find the magnetic field at the centre $O$ of the circle.

$A$ 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):

$A$ circular arc of radius $r$ carrying current $I$ subtends an angle $\frac{\pi}{8}$ at its centre. The radius of the metal wire is uniform. The magnetic induction at the centre of the circular arc is ($\mu_0 =$ permeability of free space).

What is the ratio of the electric field to the magnetic field produced by a moving point charge if its speed is $4.5 \times 10^{5} \; m/s$?

Which convention is used to represent currents and magnetic fields emerging out of a surface?

$A$ wire of length $l$ is bent into a circular loop of radius $R$ and carries a current $I$. The magnetic field at the centre of the loop is $B$. The same wire is now bent into a double loop of equal radii. If both loops carry the same current $I$ and it is in the same direction, the magnetic field at the centre of the double loop will be