An equilateral triangle of side length `l` is formed from a piece of wire of uniform resistance. The current `I` is as shown in figure. Find the magnitude of the magnetic field at its centre `O`.

Explanation

The magnetic field induction at `O` due to current through `PR` is `B_(1)=(mu_(0))/(4pi)(2l//3)/(r)[sin30^(@)+sin30^(@)]`
`=(mu_(0))/(4pi)(2l)/(3r)o.(` directed outside `)`
The magnetic field induction at `O` due to current through `PQR` is
`B_(2)=2xx(mu_(0)(l//3))/(4pir)[sin30^(@)+sin30^(@)]`
`=(mu_(0))/(4pi)(2l)/(3r)ox(` directed inside `0`
`:.` Resultant magnetic induction at `oimpliesB_(1)-B_(2)=0`