A loop consists of two identical semicircular portions of radius R, one in the x–y plane and the other in the x–z plane. The current is i. Find the magnitude of the resultant magnetic field at their common centre.
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Question

A loop consists of two identical semicircular portions of radius R, one in the x–y plane and the other in the x–z plane. The current is i. Find the magnitude of the resultant magnetic field at their common centre.

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G1 Physics · Accepted Answer

Step 1: Each semicircle produces field B₁ = B₂ = μ₀i/(4R) at the common centre. Step 2: The two semicircle planes x–y and x–z are perpendicular; hence their magnetic-field vectors are perpendicular. Step 3: Resultant magnitude B = √(B₁²+B₂²) = √2[μ₀i/(4R)] = μ₀i/(2√2R). Final answer: (A) μ₀i/(2√2 R).