The diagram shows three arrangements of circular loops, centered on vertical axes and carrying identical currents in the directions indicated. Rank the arrangements according to the magnitudes of the magnetic fields at the midpoints between the loops on the central axes.
A) 1, 2, 3
B) 2, 1, 3
C) 2, 3, 1
D) 3, 2, 1
E) 3, 1, 2

Question

The diagram shows three arrangements of circular loops, centered on vertical axes and carrying identical currents in the directions indicated. Rank the arrangements according to the magnitudes of the magnetic fields at the midpoints between the loops on the central axes. 
A) 1, 2, 3 
B) 2, 1, 3 
C) 2, 3, 1 
D) 3, 2, 1 
E) 3, 1, 2

Quizplus · Accepted Answer

The magnetic field at the midpoint of the central axis is given by:
B = μ0I/2r
where μ0 is the permeability of free space, I is the current, and r is the distance from the midpoint to the center of the loop. Since the currents are identical and the distance from the midpoint to the center of each loop is the same, the only factor affecting the magnitude of the magnetic field is the radius of the loop.
Arrangement 2 has the largest radius, followed by arrangement 3 and then arrangement 1. Therefore, the ranking of the arrangements according to the magnitudes of the magnetic fields at the midpoints between the loops on the central axis is 2, 3, 1. So, the correct answer is C.

The Diagram Shows Three Arrangements of Circular Loops, Centered on Vertical