When a helium nucleus covers a circle of radius $0.8 \,m$ in $2 \,s$, find the value of magnetic field $B$ at the centre of the circle.

Two wires $A$ and $B$ are of lengths $40 \ cm$ and $30 \ cm$. $A$ is bent into a circle of radius $r$ and $B$ into an arc of radius $r$. $A$ current $i_1$ is passed through $A$ and $i_2$ through $B$. To have the same magnetic inductions at the centre, the ratio of $i_1: i_2$ is

An element $\overrightarrow{\Delta \ell} = \Delta x \hat{i}$ is placed at the origin and carries a current of $10 \ A$. Find the magnitude of the magnetic field on the $Y$-axis at a distance of $0.5 \ m$,given $\Delta x = 1 \ cm$. (Use $\frac{\mu_0}{4 \pi} = 10^{-7} \ T \cdot m/A$)

$A$ straight wire carrying current $I$ is bent into a semi-circular arc of radius $r$,as shown. The magnitude of the magnetic field at point $O$ due to the semi-circular arc is ($\mu_{0} =$ permeability of free space).

$A$ circular current-carrying coil has radius $R$. At what distance from the centre of the coil on the axis,the magnetic induction will become $\frac{1}{8}$ th of its value at the centre of the coil?

Write the equation for the magnetic field due to a circular current-carrying loop at a point on the axis of the loop. Give its special cases.