Register to reply 
Curl and its relation to line integrals 
Share this thread: 
#1
Feb2013, 01:36 AM

P: 346

hey all
i know and understand the component of curl/line integral relation as: [tex]curlF\cdot u=\lim_{A(C)\to0}\frac{1}{A(C)} \oint_C F\cdot dr[/tex] where we have vector field [itex]F[/itex], [itex]A(C)[/itex] is the area of a closed boundary, [itex]u[/itex] is an arbitrary unit vector, [itex]dr[/itex] is an infinitely small piece of curve [itex]C[/itex] my question is, how does this definition change if i have, say [itex]curlF\cdot {x}[/itex] versus [itex]curlF\cdot {z}[/itex] where [itex]x[/itex] and [itex]z[/itex] are the unit vectors in the standard cartesian system. thanks for the feedback! you guys/girls are amazing! 


#2
Feb2013, 08:09 AM

Math
Emeritus
Sci Advisor
Thanks
PF Gold
P: 39,564

I don't understand your question. First what "definition" are you talking about? The formula you give is not a definition. Second, you are given a formula for [itex]curl F\cdot u[/itex] where u can be any unit vector but there is no reference to c on the right side they cannot be equal. Did you mean that u is the unit vector perpendicular to the plane of C? But you did not require that C be a planar curve.



#3
Feb2213, 11:16 PM

P: 346




#4
Feb2313, 12:19 AM

Mentor
P: 18,330

Curl and its relation to line integrals
I actually do like your limit definition better since it is way more intuitive. 


Register to reply 
Related Discussions  
Is any relation between curl and uniform shear available?  Differential Geometry  10  
Integrals with curl dot products  Calculus & Beyond Homework  1  
Integrals, Curl & force  Introductory Physics Homework  2  
Parametrizing and Line integrals (of a line, parabola, curve.)  Calculus & Beyond Homework  6  
Curl about an elipse. Line integral of vector field  Calculus & Beyond Homework  3 