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Question:

A current of 1A is flowing on the sides of an equilateral triangle of side 4.5 × 10⁻⁶ m. The magnetic field at the centre of the triangle will be:

8 × 10⁻⁹ Wb/m²

Zero

4 × 10⁻⁹ Wb/m²

2 × 10⁻⁹ Wb/m²

Solution:

l = 4.5 × 10⁻⁶ m
tan60° = √3 = l/2d ⇒ d = l/2√3 = (4.5 × 10⁻⁶/2√3) m
B = μ₀i/4πd (cosθ₁ + cosθ₂) = 2μ₀i/4πd (√3/2) = μ₀i/2πd (√3/2)
= μ₀i√3/4πd = μ₀i√3/4π(4.5 × 10⁻⁶/2√3)
On solving we will get option A as answer