A rectangular wire loop of length \(L\), width \(w\), and total resistance \(R\) is placed in a uniform magnetic field of magnitude \(B\) that points in the \(+z\)-direction. The loop is rotated about the \(y\)-axis with a constant angular speed \(\omega\). The \(y\)-axis passes directly through the center of the loop, bisecting the two sides of length \(w\). At time \(t = 0\), the loop lies in the \(xy\)-plane such that the area vector of the loop is parallel to the magnetic field.

Express all algebraic answers in terms of \(L\), \(w\), \(R\), \(B\), \(\omega\), \(t\), and physical constants, as appropriate.