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Curl and its relation to line integrals 
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#1
Feb2013, 01:36 AM

P: 322

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
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Thanks
PF Gold
P: 39,339

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: 322




#4
Feb2313, 12:19 AM

Mentor
P: 18,036

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


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