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, from least to greatest.
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, from least to greatest. 
A)1, 2, 3 
B)2, 1, 3 
C)2, 3, 1 
D)3, 2, 1 
E)3, 1, 2

Quizplus · Accepted Answer

According to the right-hand rule, we can determine that the magnetic fields point out of the page at the midpoint between loops 1 and 2, into the page at the midpoint between loops 2 and 3, and out of the page at the midpoint between loops 1 and 3. These directions of the magnetic fields are indicated by the X, dot, and cross symbols, respectively. Since the currents are identical, the magnitudes of the magnetic fields are proportional to the distances from the loops to the midpoints, and can be compared as follows:
- Between loops 1 and 2: B is least, halfway between the loops.
- Between loops 2 and 3: C is greatest, at the midpoint closest to loop 2.
- Between loops 1 and 3: A is in the middle, at the midpoint closest to loop 1. 
Therefore, the ranking of the arrangements from least to greatest magnetic field is 2, 3, 1, corresponding to choice C.

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