Question

A current of i ampere is flowing in an equilateral triangle of side a.The magnetic induction at the centroid will be.
ans: 9uoi/2pia

Answer 1

a = length of side of equilateral triangle

r = perpendicular distance of each side from centroid = (√3) a/6

θ = angle by each end of each side at centroid = 60

Using Biot-savart's law , magnetic field at the centroid by each side is given as

B = (μ/4π) (i/r) (Sinθ + Sinθ)

B = (μ/4π) (i/ (√3) a/6) (Sin60 + Sin60)

B = (μ/4π) (6i/ (√3) a) (2) ((√3)/2)

B = (μ/4π) (6i/a)

total magnetic field by all three sides is given as

B'' = 3 B = 3 (μ/4π) (6i/a)

B'' = (μ/2π) (9i/a)

Answer 2

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