phy-magnetism

Since the loops are identical, their magnetic flux densities should have the same magnitude, say B'

With them placed perp. to each other, the resultant magnetic flux density is given by:

B = B'√2 by Pyth thm.

So when the vertical loop is removed, the flux density at O should be:

B' = B/√2

in the downward direction by right hand grip rule.