Shown are six arrangements of long, straight wires carrying identical currents i

Question

Shown are six arrangements of long, straight wires carrying identical currents into or out of the page. The spacing between adjacent wires is either d or 2d. Rank the arrangements according to the magnitude of the net force on the underlined wire, smallest first. If two arrangements have equal force, enter them alphabetically. Please explain the solution.

Shown are six arrangements of long, straight wires carrying identical currents into or out of the page. The spacing between adjacent wires is either d or 2d. Rank the arrangements according to the magnitude of the net force on the underlined wire, smallest first. If two arrangements have equal force, enter them alphabetically. Please explain the solution.

Explanation / Answer

Let

F = the magnetic force when the distance between two wires is 2d

2F = the magnetic force when the distance between two wires is d

By right hand rules:

A: 2F
B: 2Fsqrt(2)
C: 4F
D: 0
E: Fsqrt(2)
F: 3F

Thus, in increasing order:

D, E, A, B, F, C   [ANSWER]

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