Magnetic field at center of rectangular loop

[stunner5000pt]

Find the magnetic field at the center of a rectangular loop with sides 2a and 2b.

well ok due to the sides with length 2a
$$B_{A} = \frac{\mu_{0} i}{2 \pi B} \frac{A}{\sqrt{\frac{A^2}{4} + B^2}}$$

and due to 2B sides
$$B_{B} = \frac{\mu_{0} i}{2 \pi B} \frac{B}{\sqrt{\frac{B^2}{4} + A^2}}$$

adding these two up yields the answer? Is this right? Please advise! Thanks!

 

[quantumdude]

Don't forget that magnetic fields are vectors, and so they obey vector addition. So it is not correct to add up the magnitudes of two magnetic fields unless they are parallel everywhere.

And of course it goes without saying that if your fields vary with position, then they have to be referenced to the same coordinate system.