Charge $q$ is uniformly spread on a thin ring of radius $R.$ The ring rotates about its axis with a uniform frequency $f \ Hz.$ The magnitude of magnetic induction at the center of the ring is

$A$ current loop consists of two identical semicircular parts each of radius $R,$ one lying in the $x-y$ plane and the other in the $x-z$ plane. If the current in the loop is $i,$ the resultant magnetic field due to the two semicircular parts at their common centre is

The strength of the magnetic field at a point $r$ near a long straight current-carrying wire is $B$. The field at a distance $\frac{r}{2}$ will be

Find the magnetic field at the centre $P$ of a square loop of side length $20 \, cm$ carrying a current of $3 \, A$.

Two identical current-carrying coils with the same center are placed with their planes perpendicular to each other. If current $I = \sqrt{2} \text{ A}$ and the radius of the coil is $R = 1 \text{ m}$,then the magnetic field at the center is equal to (where $\mu_0$ is the permeability of free space).

Discuss the similarities and differences between the Biot-Savart law and Coulomb's law.