Q. A current loop consists of two identical semicircular parts each of radius R, one lying in the x-y plane and the other in x-z plane. If the current in the loop is i. The resultant magnetic field due to the two semicircular parts at their common centre is
A) μ₀i/(2√2 R)
B) μ₀i/(2R)
C) μ₀i/(4R)
D) μ₀i/(√2 R)
Explanation
[Solution from source] Each semicircle gives μ₀i/(4R) at the centre, half the field of a full loop. Because the two semicircles lie in perpendicular planes, their fields are perpendicular, so the resultant is √2 × μ₀i/(4R) = μ₀i/(2√2 R). Simply adding the two fields gives μ₀i/(2R), which wrongly treats them as parallel. Answer (1).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.