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

Using the right-hand rule for the direction of the magnetic field, we can see that the magnetic field due to the quarter circle with radius 3r is the greatest since the magnetic field lines are concentrated in a smaller area around point C. The magnetic field due to the half circle with radius 2r is next because it has a larger radius and thus the field lines are more spread out. The magnetic field due to the quarter circle with radius r is the least since it has the largest radius and thus the field lines are the most spread out. Therefore, the ranking from least to greatest is 3, 2, 1.

The Diagrams Show Three Circuits Consisting of Concentric Circular Arcs