An equilateral triangular loop of side ℓ carries current i. If the magnetic field at its circumcentre is written B=μ₀αi/(4πℓ), find α.
Physics · Magnetic effect of current
JEE Advanced

Question

An equilateral triangular loop of side ℓ carries current i. If the magnetic field at its circumcentre is written B=μ₀αi/(4πℓ), find α.

G1 Physics · Accepted Answer

Distance of the centre from each side is ℓ/(2√3). Field of one side is μ₀i/(4πr)(sin 60°+sin 60°)=3μ₀i/(2πℓ). Three sides give B=9μ₀i/(2πℓ)=μ₀i(18)/(4πℓ). Hence α=18.