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

[flyingpig]

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?

 

[eczeno]

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.

 

[flyingpig]

Then what's wrong if you take the integral from a to c?

 

[eczeno]

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.