Bending Wires and Magnetic Fields?

[albert1993]

Homework Statement

see attached. this question is from a test that doesn't allow any calculators and usually makes students solve the problem in 1 minute max.

Homework Equations

perhaps biot savart is to be used? but I doubt that can be done in the time limit...

The Attempt at a Solution

Only the verticals affect the center? I don't know...

 

[praharmitra]

Only the verticals affect the center. For the horizontals, by simple symmetry arguments would you agree that the magnetic field due to a half wire will be half that of a full wire? If so, then you are done!

 

[albert1993]

Thank you!