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What is the difference between closed integration and opened integration ?

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yousefsam

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Pls i have a question, it seems desired for me .
my question in electromagnetic :
Q : What is the difference between closed integration and opened integration ?
this question seems easy but i can't understand why we take closed integration to find manetic field inensity :
∫H dl = N i ; but this integration along closed path .
but when we want to find flux density , we take opened integration :
∫B dA = Φ .
thaks all .
 

Re: hello guys

Closed integration in ∫H dl = N i refers to taking the integral path so that it starts and ends at the same point. While the open integration in ∫B dA = Φ means you have to take a piece of area and integrate over it. the fist one is closed in terms of dl since it starts and ends at the same l, while the second one which integrates over an area does not close up to any space.
Putting it another way, in the 1st integral no matter how you integrate the vector space of l that you integrate will form a closed space (a circle or any closed contour), while in the second integral the area vectors that you integrate will not form a closed space (eg a sphere), For Gauss Law you have to do a closed area integration.
I hope I understood your confusion?
 

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