# Magnetic Field Due to a Curved Wire Segment

• ChiralSuperfields
In summary, the conversation discussed the use of limits of integration for an integral over the curved path AC. The text did not explicitly state the limits of integration, but the solution could be written as ##\int_S##, where S is the curve AC. The use of a line integral to denote summing the length elements over the path was also mentioned, but this symbol is typically used for integrating around a closed loop.

#### ChiralSuperfields

Homework Statement
Relevant Equations
For this problem,

The solution is,

However, why did they not use limits of integration for the integral in red? When I solved this, I used

as limits of integration.

I see that is not necessary since you get the same answer either way, but is there a deeper reason?

Many thanks!

The text says "integrate over the curved path AC", so it was not essential to write that in the algebra. Also, one does not always have to specify the integration domain as a pair of endpoints. They could have defined S as the curve AC and written ##\int_S##.

MatinSAR and ChiralSuperfields
haruspex said:
The text says "integrate over the curved path AC", so it was not essential to write that in the algebra. Also, one does not always have to specify the integration domain as a pair of endpoints. They could have defined S as the curve AC and written ##\int_S##.
Thanks for your help @haruspex ! That second notation you mention makes more sense than their single integral over ds. I think another way to avoid implicitly defining an integration domain is by using a line integral
to denote that we are summing the length elements over the path, correct?

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Callumnc1 said:
Thanks for your help @haruspex ! That second notation you mention makes more sense than their single integral over ds. I think another way to avoid implicitly defining an integration domain is by using a line integral View attachment 320352to denote that we are summing the length elements over the path, correct?
No, that symbol is for integrating around a closed loop.

hutchphd and ChiralSuperfields
haruspex said:
No, that symbol is for integrating around a closed loop.
Oh, thank you for your help @haruspex !

hutchphd