Physics
Physics
Problem
Three identical coaxial circular loops, each of radius , are placed side by side so that the distance between the centres of successive loops is negligible compared with the radius. Each loop carries a current of in the same direction. a. (i) Determine the magnitude of the magnetic field at the common centre on the common axis due to the combination of the three loops. b. (ii) State the direction of the resultant magnetic field at that point. c. (iii) If the current in the middle loop alone is reversed while keeping the outer two unchanged, calculate the new magnitude of the resultant field at the centre and specify its direction.Intuitive explanation
The key here is recognizing that when coaxial loops are very close together, you can treat them almost as a single system and use superposition. The magnetic field on the axis of a current loop has a well-known formula, and since all three loops carry current in the same direction, their fields add constructively at any point along the axis. Calculate the field from one loop at your point of interest, then multiply by three—this is much faster than integrating each loop separately.
Intuitive explanation
The key here is recognizing that when coaxial loops are very close together, you can treat them almost as a single system and use superposition. The magnetic field on the axis of a current loop has a well-known formula, and since all three loops carry current in the same direction, their fields add constructively at any point along the axis. Calculate the field from one loop at your point of interest, then multiply by three—this is much faster than integrating each loop separately.