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 ) [ sin 30^@ + sin 30^@]`
`= (mu_0 )/(4pi) (2l)/(3r) o. ` (directed outside)
The magnetic field induction at O due to current through PQR is
` B_2 = 2 xx (mu_0 (l//3) )/(4pi r) [ sin 30^@ + sin 30^@ ]`
` = (mu_0)/(4pi) (2l)/(3r) ox` (directed inside)
` therefore ` Resultant magnetic induction at `O rArr B_1 - B_2 = 0`