Answer
We can rank the arrangements according to the magnitude of the net magnetic field at the center of the square:
$(c) \gt (d) \gt (a) = (b)$
Work Step by Step
We can write the expression for the magnetic field produced by a current in a straight wire:
$B = \frac{\mu_0~i}{2~\pi~R}$
Let $R$ be the distance from the center of the square to each corner.
(a)
By the right hand rule, the magnetic field due to the current at opposite corners cancel out since the magnetic fields are in opposite directions.
$B_{net} = 0$
(b) By the right hand rule, the magnetic field due to the current at opposite corners cancel out since the magnetic fields are in opposite directions.
$B_{net} = 0$
(c)
By the right hand rule, the magnetic field due to the current at opposite corners add together since the magnetic fields are in the same directions.
$B_{net} \gt 0$
(d)
By the right hand rule, the magnetic field due to the two currents out of the page at opposite corners cancel out since the magnetic fields are in opposite directions. By the right hand rule, the magnetic field due to the currents at opposite corners, with one current into the page and one current out of the page, add together since the magnetic fields are in the same directions.
$B_{net} \gt 0$
Note that the net magnetic field in situation (c) is greater than the net magnetic field in situation (d) because in situation (d), the magnetic fields due to one pair of currents cancel out.
We can rank the arrangements according to the magnitude of the net magnetic field at the center of the square:
$(c) \gt (d) \gt (a) = (b)$
