Question

A long wire is bent in the shape of circular coil without cross contact at p.a current is passed through it .calculate the magnetic field at the centre?

Answer 1

we apply the Biot-SAVART's law for magnetic field (flux density ) dB due to a length dl at a distance r from dl :

Radius = r.

$\vec{dB}=\frac{\mu_0 i}{4\pi}\frac{\vec{dl}X\hat{r}}{r^2}\\\\\vec{dB} \perp coil\ (ie.,\ along\ axis,\ right\ hand\ thumb\ rule)=same\ for\ all\ dl.\\\\dB=\frac{\mu_0 i\ dl}{4 \pi r^2}\\\\Integrate\ over\ circumference\\\\B=\frac{\mu_0 i\ 2\pi\ r}{4 \pi r^2}=\frac{\mu_0\ i}{2\ r}$