Let F? =(5z+5x4)i? +(6y+7z+7sin(y4))j? +(5x+7y+6ez4)k? . (a) Find curl F? . curl

Question

Let F? =(5z+5x4)i? +(6y+7z+7sin(y4))j? +(5x+7y+6ez4)k? .

(a) Find curl F? .
curl F? = 0

(b) What does your answer to part (a) tell you about ?CF? ?dr?  where C is the circle (x?10)2+(y?15)2=1 in the xy-plane, oriented clockwise?
?CF? ?dr? = 0

(c) If C is any closed curve, what can you say about ?CF? ?dr? ?
?CF? ?dr? = 0

(d) Now let C be the half circle (x?10)2+(y?15)2=1 in the xy-plane with y>15, traversed from (11,15)to (9,15). Find ?CF? ?dr?  by using your result from (c) and considering C plus the line segment connecting the endpoints of C.
?CF? ?dr? =

need help with C

Explanation / Answer

c)
Because the field is conservative, i,e curl F = 0,
we can state that integral F.dr will be PATH INDEPENDENT, it wont depend on the path, no matter what the path is, the value will always be the same

Related Questions

Navigate

• Browse (All)
• Browse L
• Subjects