If a thin uniform wire of length 1 m is bent into an equilateral triangle and carries a current of `sqrt3A` in anitclockwise direction, find the net magnetic induction at the centroid

Explanation

`B_("net") = 3B_("each side") ` ,
`B_("net") = 3 (mu_0)/(4pi) xx I/r (sin 60^@ + sin 60^@) `

`(because r = (a)/(2 sqrt3) = 3 xx (mu_0)/(4pi) I/r (2 sin 60^@)`
` = 3 xx (mu_0)/(4pi) (I(2sqrt3) )/(a) 2 xx (sqrt3)/(2) = 18 (mu_0)/(4pi) I/a`
`B = 18 xx 10^(-7) xx (sqrt3)/(1//3) = 54 sqrt3 xx 10^(-7) T`