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.