An equilateral triangular loop of wire of side / carries a current I. The magnetic field produced at the circumcentre of the loop is

Options

A. `(mu_(0))/(4pi) (3sqrt3I)/(I)`
B. `(mu_(0))/(4pi) (9I)/(I)`
C. `(mu_(0))/(4pi) (18I)/(I)`
D. `(mu_(0))/(4pi) (6I)/(I)`

Answer

C

Explanation

If l is the side of the triangle , the dustance of the circumcentre from each of the side of the triangle is `r=(1)/(3)l sin60^(@)=(1sqrt3)/(6)`
The magnetic induction at the curcumcentre O due to each of the side of the triangle carrying a current I is
`B=(mu_(0))/(4pi)(I)/(r)(sin60^(@)+sin60^(@))=(mu_(0))/(4pi)(18I)/(l)`