Solution
= Solution
The field is $e_\theta$, so on the polar boundary $F\cdot dr=r\,d\theta$. Hence
$$
\boxed{\oint_CF\cdot dr=\int_{-\pi}^{\pi}(1+\cos\theta)\,d\theta=2\pi.}
$$
= Solution
The field is $e_\theta$, so on the polar boundary $F\cdot dr=r\,d\theta$. Hence
$$
\boxed{\oint_CF\cdot dr=\int_{-\pi}^{\pi}(1+\cos\theta)\,d\theta=2\pi.}
$$