Chapter 3, Problem 3.28P

Suppose you have the field $H=r\cos \theta a_{\varphi }A/m$. Now consider the cone specified by $\theta =\pi /4$, with a height a as shown in Figure 3.56. The circular top of the cone has a radius a. (a) Evaluate the right side of Stoke’s theorem through the $dS=dS{a}_{\theta }$ surface. (b) Evaluate the left side of Stoke’s theorem by integrating around the loop.

Figure 3.56 Cone for Problem 3.28.