A current carrying wire $\mathrm{AB}$ of the length $2\pi R$ is turned along a circle, as shown in figure. The magnetic field at the centre $O$.

A battery is connected between two points $\mathrm{A}$ and $\mathrm{B}$ the circumference of a uniform conducting ring of radius $r$ and resistance $R$. One of the arcs $\mathrm{AB}$ of the ring subtends an angle $\mathrm{\theta }$ at the centre. The value of the magnetic induction at the centre due to the current in the ring is:

Figure shows an amperian path $\mathrm{ABCDA}$. Part $\mathrm{ABC}$ is in vertical plane $\mathrm{PSTU}$ while part $\mathrm{CDA}$ is in horizontal plane $\mathrm{PQRS}$. Direction of circumlation along the path is shown by an arrow near point $\mathrm{B}$ and at$\mathrm{D}.$ $\oint \hat{\mathrm{B}}. \mathrm{d} \hat{\mathrm{l}}$  for this path according to Ampere’s law will be :

A current $I$ flows along the length of an infinitely long, straight and thin-walled pipe. Then