The diagrams show three circuits consisting of concentric circular arcs (either half or quarter circles of radii r, 2r, and 3r)and radial lengths.The circuits carry the same current.Rank them according to the magnitudes of the magnetic fields they produce at C, least to greatest.
A)1, 2, 3
B)3, 2, 1
C)1, 3, 2
D)2, 3, 1
E)2, 1, 3

Question

The diagrams show three circuits consisting of concentric circular arcs (either half or quarter circles of radii r, 2r, and 3r)and radial lengths.The circuits carry the same current.Rank them according to the magnitudes of the magnetic fields they produce at C, least to greatest. 
A)1, 2, 3 
B)3, 2, 1 
C)1, 3, 2 
D)2, 3, 1 
E)2, 1, 3

Quizplus · Accepted Answer

The magnetic field produced by a current-carrying wire is proportional to the radius of the wire. Since all three circuits carry the same current, the one with the largest radius (circuit 3) will produce the greatest magnetic field at point C. Similarly, the circuit with the smallest radius (circuit 1) will produce the least magnetic field at point C. Therefore, the ranking from least to greatest is circuit 1, circuit 2, and circuit 3, which corresponds to option B.

The Diagrams Show Three Circuits Consisting of Concentric Circular Arcs