A wire carrying current I has two very long straight portions parallel to the x-axis and a semicircular portion of radius R in the y–z plane, as shown. Find the magnetic field vector at O. [Image]
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A wire carrying current I has two very long straight portions parallel to the x-axis and a semicircular portion of radius R in the y–z plane, as shown. Find the magnetic field vector at O. [Image]

G1 Physics · Accepted Answer

Step 1: For a semicircular arc of radius R, magnetic field magnitude at the centre is B_arc = μ₀I/(4R). Its direction follows the right-hand rule and is −î in the displayed y–z geometry. Step 2: The two semi-infinite straight arms contribute a total B_straight = μ₀I/(2πR) along −k̂ according to the drawn current directions. Step 3: Combine orthogonal Cartesian components: B⃗ = −[μ₀I/(4R)]î − [μ₀I/(2πR)]k̂. Step 4: Factor μ₀I/(4πR): B⃗ = −[μ₀I/(4πR)](πî + 2k̂). Final answer: (A) −μ₀I/(4πR) ×…