Calculating the circulation of the Field F along the borders of this region

  • Thread starter Thread starter Amaelle
  • Start date Start date
  • Tags Tags
    Circulation Field
Amaelle
Messages
309
Reaction score
54
Homework Statement
look at the image
Relevant Equations
stocks theorem
Greetings
The exercice consist of calulating the circuitation of the Field F along a the borders of the region omega

my problem was how they found that y goes from 0 to h ( for 0 it´s clear but the mystery for me is h)

Thank you!

1644438807381.png
 
Physics news on Phys.org
Compute the intersection between the curves ##x^2 + y^2 = h + h^2## and ##x = \sqrt y##.

Also, it is ”Stokes’ theorem” (or in the two-dimensional case, Green’s formula in the plane).
 
  • Like
Likes Delta2
Orodruin said:
Compute the intersection between the curves ##x^2 + y^2 = h + h^2## and ##x = \sqrt y##.

Also, it is ”Stokes’ theorem” (or in the two-dimensional case, Green’s formula in the plane).
yes indeed we get
y^2+y-(h^2+h)=0
we use descriminant Δ=1-4(h^2+h)
y=[1+(-)sqrt(4(h^2+h))]/2 which is ugly
is there any simplification ?

thank you!
 
Amaelle said:
yes indeed we get
y^2+y-(h^2+h)=0
we use descriminant Δ=1-4(h^2+h)
y=[1+(-)sqrt(4(h^2+h))]/2 which is ugly
is there any simplification ?

thank you!
If ##y^2 + y = h^2 + h##, then it should be fairly obvious that ##y=h## is a solution.
 
  • Love
Likes Amaelle
Orodruin said:
If ##y^2 + y = h^2 + h##, then it should be fairly obvious that ##y=h## is a solution.
thank you, I really didn´t see it!
 
Amaelle said:
thank you, I really didn´t see it!
To add to Oro's great hint:
Maybe factor :
## y^2-h^2=-(y-h)##?
 
  • Love
Likes Amaelle
WWGD said:
To add to Oro's great hint:
Maybe factor :
## y^2-h^2=-(y-h)##?
amazing! thank you!
 

Similar threads

Replies
2
Views
1K
Replies
2
Views
2K
Replies
5
Views
1K
Replies
2
Views
3K
Replies
1
Views
1K
Replies
2
Views
1K
Replies
8
Views
2K
Replies
7
Views
2K
Back
Top