Answer
We can rank the situations according to the magnitude of the force required of us:
$(1) \gt (2) \gt (4) \gt (3)$
Work Step by Step
We can assume that the resistance of the loop is proportional to the total length of the loop.
We can write a general expression for the force on a loop:
$F = \frac{B^2~L^2~v}{R}$
We can write an expression for the force on each loop:
(1) $F = \frac{B^2~(2L)^2~v}{6R} = \frac{2}{3}~\frac{B^2~L^2~v}{R}$
(2) $F = \frac{B^2~(2L)^2~v}{8R} = \frac{1}{2}~\frac{B^2~L^2~v}{R}$
(3) $F = \frac{B^2~L^2~v}{6R} = \frac{1}{6}~\frac{B^2~L^2~v}{R}$
(4) $F = \frac{B^2~L^2~v}{4R} = \frac{1}{4}~\frac{B^2~L^2~v}{R}$
We can rank the situations according to the magnitude of the force required of us:
$(1) \gt (2) \gt (4) \gt (3)$
