A long straight conductor contains a semicircular arc of radius π/10 m carrying current I = 3 A. The magnitude of magnetic field at the centre O of the arc is:
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Question

A long straight conductor contains a semicircular arc of radius π/10 m carrying current I = 3 A. The magnitude of magnetic field at the centre O of the arc is:

G1 Physics · Accepted Answer

For a circular arc subtending angle θ at the centre, B = μ₀Iθ/(4πR) For a semicircle, θ = π: B = μ₀I/(4R) = (4π × 10⁻⁷ × 3) / [4 × (π/10)] = 3 × 10⁻⁶ T = 3 μT The straight portions lie along the line through O, so their contribution at O is zero. Hence option D.