Question:** An electrical engineer analyzes the magnetic flux through a coil whose area vector \( \vecA \) rotates in the \( xy \)-plane. If \( \vecA(t) = A_0 \cos(\omega t) \hat\mathbfx + A_0 \sin(\omega t) \hat\mathbfy \) and the magnetic field is \( \vecB = B_0 \hat\mathbfz \), compute the time average of the magnetic flux \( \Phi_B = \vecB \cdot \vecA(t) \) over one period. - Crosslake