Integrating a Uniform Magnetic Field: Solving for ∫Bdl

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Homework Help Overview

The discussion revolves around evaluating the integral of a uniform magnetic field, specifically the expression ∫Bdl. Participants are exploring the implications of the uniformity of the magnetic field on the integral's evaluation.

Discussion Character

  • Exploratory, Mathematical reasoning

Approaches and Questions Raised

  • The original poster attempts to simplify the integral by factoring out the uniform magnetic field B, leading to the expression B∫dl. Some participants discuss the interpretation of ∫dl in the context of a circular path, questioning whether it corresponds to the circumference of the circle.

Discussion Status

Participants are actively engaging with the problem, with some providing supportive feedback on the original poster's reasoning. There is a suggestion that the integral ∫dl could represent the circumference of a circle, indicating a productive line of inquiry.

Contextual Notes

There is an implicit assumption that the path of integration is circular, and the radius R is relevant to the evaluation of the integral. The discussion does not resolve the integral but explores its components and interpretations.

Mdhiggenz
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Homework Statement



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I already worked out the right hand side. What is giving me problems is figuring out the left hand side, ∫Bdl

Since B is uniform, it can be removed from the integral leaving B∫dl

now I'm stuck.





Homework Equations





The Attempt at a Solution

 
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Mdhiggenz said:
What is giving me problems is figuring out the left hand side, ∫Bdl

Since B is uniform, it can be removed from the integral leaving B∫dl

now I'm stuck.

∫dl is just the sum of all the elements of length around the circle of radius R. Your work up to this point looks good to me.
 
in that case would it simply be 2pir?
 
Yes, with r = R.
 
Thanks TSny.
 

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