Chapter 3, Problem 52P

Verify Stokes’s theorem for the vector field

$B=(\hat{r}r\cos \varphi +\hat{\varphi }\sin \varphi )$

by evaluating the following:

(a) ${\displaystyle \underset{C}{\oint }B \cdot dl}$ over the semicircular contour shown in Fig. P3.52(a).

(b) ${\displaystyle \underset{S}{\int }(\nabla \times B)\cdot d\text{s}}$over the surface of the semicircle.