{[ promptMessage ]}

Bookmark it

{[ promptMessage ]}

# s10 - Solution to Set 10 1(a F = 2 F =(x y y x)k = 0(b F =...

This preview shows page 1. Sign up to view the full content.

Solution to Set 10 1. (a) ∇ · F = 2 ∇ × F = ( x y y x ) k = 0 (b) ∇ · F = y 2 ( x 2 + y 2 ) 3 / 2 + x 2 ( x 2 + y 2 ) 3 / 2 = 1 x 2 + y 2 ∇ × F = xy ( x 2 + y 2 ) 3 / 2 + xy ( x 2 + y 2 ) 3 / 2 k = 0 (c) ∇ · F = 0 ∇ × F = 2 k (d) F is not differentiable on the circle x 2 + y 2 = 1. ∇ · F = 0 for x 2 + y 2 < 1 0 for x 2 + y 2 > 1 ∇ × F = 2 k for x 2 + y 2 < 1 x 2 y 2 ( x 2 + y 2 ) 2 x 2 y 2 ( x 2 + y 2 ) 2 k = 0 for x 2 + y 2 > 1 2. ∇ · fF = 3 e x + y + z ∇ × fF = 0 3. Let F 1 , F 2 , F 3 be the components of F . The x component of ∇ × ( φ F ) is y ( φF 3 ) z ( φF 2 ) = φ ( y F 3 z F 2 )+ ( φ y F 3 φ z F 2 ). It is the same as the x component of φ ∇ × F + φ × F . Similarly, the same can be shown for the y and z components. 4. ∇ ·
This is the end of the preview. Sign up to access the rest of the document.

{[ snackBarMessage ]}

Ask a homework question - tutors are online