Problem 3.291

A thin wire \(A C\) shaped as a semi-circle of diameter \(d=\) \(=20 \mathrm{~cm}\) rotates with a constant angular velocity \(\omega=100 \mathrm{rad} / \mathrm{s}\) in a uniform magnetic field of induction \(B=5.0 \mathrm{mT}\), with \omega \(\uparrow \uparrow\). The rotation axis passes through the end \(A\) of the wire and is perpendicular to the diameter \(A C .\) Find the value of a line integral \(\int \mathbf{E} d \mathbf{r}\) along the wire from point \(A\) to point \(C .\) Generalize the obtained result.