Why is it the integral from a to b, but not a to c?

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Homework Help Overview

The discussion revolves around the application of integrals in the context of electric potential in a capacitor setup, specifically questioning the limits of integration from a to b versus a to c.

Discussion Character

  • Conceptual clarification, Assumption checking

Approaches and Questions Raised

  • The original poster questions why the integral is defined from a to b instead of a to c, seeking clarification on the reasoning behind the chosen limits. Some participants explain the significance of the region between the plates of the capacitor and the behavior of the electric field in different regions.

Discussion Status

Participants are exploring the reasoning behind the limits of integration, with some providing insights into the nature of the electric field in the capacitor. There is a recognition that integrating from a to c yields the same result due to the electric field being zero in that region, but the discussion remains open regarding the implications of the chosen limits.

Contextual Notes

There is an emphasis on the behavior of electric fields in different regions, particularly noting that the electric field is absent in certain areas, which influences the choice of integration limits.

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Homework Statement



[PLAIN]http://img225.imageshack.us/img225/3342/unledyk.png





The Attempt at a Solution



The solution is posted with the problem.

My question is that why is the integral from a to b and not a to c? Why are they summining the potential from a to b?
 
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hello,

the region from a to b is the 'between the plates' part of the capacitor, so that is where the electric field can be found. both the sphere and shell are conductors so there will be no e-field inside those regions.

also, they are not 'summing the potential'; that is a line integral of the e-field over a path from the surface of the sphere to the inner surface of the shell. since the electric force is conservative, the result will be the same no matter what path is chosen.
 
Then what's wrong if you take the integral from a to c?
 
you can do that if you want, but the electric field between b and c is zero, so it will contribute nothing to the integral and you will get the same result.
 

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