Help with the conventions used for curl operator

[ppoonamk]

http://web.mit.edu/6.013_book/www/chapter2/2.4.html

I was going through the curl derivation on the above link. How does equation 3 turn out? Δy is the incremental length. But how do you decide whether it is +Δy/2 or -Δy/2. And why is the line integral taken Δz when the change is in the y direction. I am utterly confused :(

 

[Ray Vickson]

http://web.mit.edu/6.013_book/www/chapter2/2.4.html

I was going through the curl derivation on the above link. How does equation 3 turn out? Δy is the incremental length. But how do you decide whether it is +Δy/2 or -Δy/2. And why is the line integral taken Δz when the change is in the y direction. I am utterly confused :(

The component A_y is integrated left-to-right along the bottom of the square (where z = -Δz/2, and y goes from -Δy/2 to +Δy/2), and also along the top of the square from right-to-left.

RGV

 

[ppoonamk]

Sorry I still did not understand you properly :( Please forgive my ignorance about this. What is
+Δy/2 and -Δy/2. Why is the entire Ay compnonent have a 1 sign before it. AT the bottom of the sqyare on the left z is -Δz/2 but the first component of Ay has +Δz/2 term

 

[ppoonamk]

I understood. Thank you :)