A flat coil consisting of \(80\) turns of wire has a cross-sectional area of \(5.0 \times 10^{-3} \text{ m}^2\) and a total electrical resistance of \(2.0 \text{ }\Omega\). The coil is initially placed in a uniform magnetic field of magnitude \(0.30 \text{ T}\) such that the plane of the coil is perpendicular to the magnetic field lines. The coil is then flipped by \(180^\circ\) about an axis lying in its plane over a time interval of \(0.040 \text{ s}\). What is the total electric charge that flows through any cross section of the coil wire during this rotation?