The current passing through a conducting loop in the form of equilateral triangle of side 4 3 ~cm is 2 A. The magnetic field at its centroid is 10⁻⁵ ~T . The value of is _ _ _ _ . (Given : _ o =4 10⁻⁷ SI units)

Step-by-step solution

For an equilateral triangle of side a , the distance of the centroid from any side is r = a 2 3 . Given side a = 4 3 cm = 4 3 10⁻² m. So, r = 4 3 10⁻² 2 3 = 2 10⁻² m. The magnetic field at the centroid due to one side of the triangle is B₁ = ₀ I 4 r ( ₁ + ₂) . For an equilateral triangle, ₁ = ₂ = 60^ . B₁ = 10⁻⁷ 2 2 10⁻² ( 60^ + 60^ ) = 10⁻⁵ ( 3 2 + 3 2 ) = 3 10⁻⁵ T. The total magnetic field at the centroid due to all three sides is B = 3B₁ = 3 3 10⁻⁵ T. Comparing with B = 10⁻⁵ T, we get = 3 3 .