A very long current-carrying wire is bent into a semicircular arc from A to B, with two long straight tangential portions as shown. Find the magnetic field at the centre P and its direction. [Image]
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A very long current-carrying wire is bent into a semicircular arc from A to B, with two long straight tangential portions as shown. Find the magnetic field at the centre P and its direction. [Image]

G1 Physics · Accepted Answer

Step 1: A semicircular current arc of radius R subtends angle π at P. Its field has magnitude B_arc = μ₀Iπ/(4πR) = μ₀I/(4R). Step 2: Each infinitely long straight tangential arm contributes μ₀I/(4πR), and both arms contribute in the same direction. Combined straight-part field: B_straight = μ₀I/(2πR). Step 3: The arc and straight-arm fields are oppositely directed at P. Their difference is B_net = μ₀I/(4R) − μ₀I/(2πR) = [μ₀I/(4R)](1 − 2/π). Step 4: The right-hand rule gives direction away from…