# Why does magnetic flux linkage become negative when a coil is turned through 180degrees?

Taking a rectangular coil, in a constant magnetic field, it is understandable that BANcos(theta) should apply for the magnitude of the flux linkage. However if the coil is turned through 180 degrees why should the flux linkage then become negative, implying that the emf induced is also negative? As flux linkage is defined in terms of the area swept out, I do not see how this could come about beig negative as the ending position seems to be equivelent to the starting one in terms of B, A and N.

• That's exactly right. Think $\vec{B}\cdot \vec{A}$ and it all makes sense. – Floris Mar 26 '15 at 19:03