Three concentric conductors, one grounded (Potential)

[jegues]

Homework Statement

See figure attached.

Homework Equations

The Attempt at a Solution

See figure attached.

I'm confused how they deduced that V1-V2 is going to be the integral of the electric field from a to b.

How do they choose the path from a to b?

How can they say that the electric field integrated over this path is going to be V1-V2?

I express the same confusion over the 2nd integral, why is V2 equal to the electric field integrated from c to d?

 

[Matterwave]

The path doesn't matter. Since this is an electro-static problem, the E field is a conservative field, meaning that integrals are path independent. You can find a proof of this in most elementary E&M texts. The voltage between two points is the path integral of E between those two points, that is how it is defined.