The current passing through a conducting loop in the form of equilateral triangle of side 4√3 cm is 2A. The magnetic field at its centroid is α × 10⁻⁵ T. The value of α i $s ______.$
(Given : μ₀ = 4π × 10⁻⁷ SI units)

Question

The current passing through a conducting loop in the form of equilateral triangle of side 4√3 cm is 2A. The magnetic field at its centroid is α × 10⁻⁵ T. The value of α i $s ______.$

(Given : μ₀ = 4π × 10⁻⁷ SI units)

G1 Physics · Accepted Answer

For an equilateral triangle of side a = 4√3 cm, the perpendicular distance from the centroid to each side is d = a√3/6 = (4√3)(√3)/6 cm = 2 cm = 2×10⁻² m. For one finite side, the magnetic field at the centroid is B₁ = [μ₀I/(4πd)](sin60° + sin60°). Thus, B₁ = [μ₀I/(4πd)]√3. All three sides produce magnetic fields in the same perpendicular direction. Therefore, B = 3B₁. Substitute μ₀ = 4π×10⁻⁷, I = 2 A, d = 2×10⁻² m. Hence, B = 3 × [(4π×10⁻⁷)(2)/(4π×2×10⁻²)]√3 = 3√3×10⁻⁵ T. Therefore, α = 3√3. C…

The current passing through a conducting loop in the form of equilateral triangle of side 4√3 cm is 2A. The magnetic field at its centroid is α × 10⁻⁵ T. The value of α i s ______. (Given : μ₀ = 4π × 10⁻⁷ SI units)