A wire of total length L is bent into a regular n-sided polygon and carries current I. What is the magnetic field at the centre?
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A wire of total length L is bent into a regular n-sided polygon and carries current I. What is the magnetic field at the centre?

G1 Physics · Accepted Answer

For one side, perpendicular distance to the centre is a=[L/n]/[2tan(π/n)]. The half-side subtends angle π/n, so Bside=μ₀I sin(π/n)/(2πa). Multiplying by n gives B=μ₀I n² sin(π/n)tan(π/n)/(πL).