Answer
We can rank the Amperian loops according to the magnitude of $~~\int~B\cdot ds~~$ around each:
$b \gt a \gt d \gt c$
Work Step by Step
$\int~B\cdot ds = \mu_0~i_{enc}$
We can write an expression for the magnitude of $~~\int~B\cdot ds = \mu_0~i_{enc}~~$ for each loop.
(a) $\int~B\cdot ds = (\mu_0)~(4~A)$
(b) $\int~B\cdot ds = \vert (\mu_0)~(4~A - 9~A) \vert = (\mu_0)~(5~A)$
(c) $\int~B\cdot ds = (\mu_0)~(4~A - 9~A+5~A) = (\mu_0)~(0)$
(d) $\int~B\cdot ds = \vert (\mu_0)~(4~A - 9~A+5~A-3~A)\vert = (\mu_0)~(3~A)$
We can rank the Amperian loops according to the magnitude of $~~\int~B\cdot ds~~$ around each:
$b \gt a \gt d \gt c$
