Determine the magnitude of magnetic field at the centre of the current carrying wire arrangement shown in the figure. The arrangement extends to infinity. (The wires joining the successive squares are along the line passing through the centre) (Assume negligible gap while wire is turned into squares)

 

 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 :