It turns out that a simple way to describe the emf in any of these situations is in terms of the change in magnetic flux through the loop in Figures 20-2 and 20-3. We define this in the same way that we defined electric flux in Section 16-6: It’s the area \(A\) of the surface outlined by the loop, multiplied by \(B \cos{\theta}\), the component of the magnetic field that’s perpendicular to that surface (see part (a) of Figure 20-4). In equation form, the magnetic flux \(\Phi_B\) (“phi-sub-B”) through the loop is
(The subscript \(B\) reminds us that this is the flux of the magnetic field \(\vec{B}\).) As parts (b) and (c) of Figure 20-4 show, the flux \(\Phi_B\) can be positive or negative.