In this problem, you will determine an expression for curl F in spherical coordinates
Chapter 7, Problem 33(choose chapter or problem)
In this problem, you will determine an expression for curl F in spherical coordinates. Let F be a vector field of class C1, and write F = F e + F e + F e . Show that e curl F = 1 sin (sin F ) F , e curl F = 1 1 sin F (F ) , and e curl F = 1 (F) F by using Exercise 31 and the three paths shown in Figure 7.51. Conclude that curl F = 1 2 sin e e sin e / / / F F sin F . (See Theorem 4.6 of Chapter 3.)
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