Q. Two similar coils of radius R are lying concentrically with their planes at right angles to each other. The currents flowing in them are I and 2I, respectively. The resultant magnetic field induction at the centre will be
A) μ₀I/R
B) √5 μ₀I/(2R)
C) 3μ₀I/(2R)
D) μ₀I/(2R)
Explanation
[Solution from source] The coils give fields μ₀I/(2R) and μ₀(2I)/(2R) = μ₀I/R at the centre, and these are perpendicular because the coil planes are perpendicular. Resultant B = √[(μ₀I/2R)² + (μ₀I/R)²] = √5 μ₀I/(2R). Simply adding them (3μ₀I/2R) ignores that the fields are at right angles. Answer (2).
Reviewed by Dr. Abubacker
Physics Educator & NEET/JEE Specialist
Ph.D. in Physics with 19+ years of teaching experience.