Electromagnetic fields: Eletric potential inside a non conductive sphere

[GhostStudent]

Homework Statement

Hello all;
i am trying to calculate the potential, inside a non conductive sphere of radius equal to a, in a point at a distance r from the center of the sphere.

Homework Equations

i know that:

where E and s are vectors;
and that the Eletric field inside the sphere is:

The Attempt at a Solution

since the distance r is:
0<r<a
i changed the limits so that:

but here comes the part were i am stuck:
i found:

but the correct answer, so far, should be

which means that the first integral [

] should be equal to zero, but i can't seem to understand why

thx in advance.
p.s.:
please tell me if the images are not showing up.

 

[kuruman]

It is not clear why you have two line integrals. You should use

[tex]\varphi(r)-\varphi(a)=-\int^{r}_{a}\vec{E}\cdot \vec{ds}[/tex]

 

[GhostStudent]

i guess i was thinking more on terms of the path i should take, that's why my first integral ranges from 0 to a (size of the sphere), but since r is greater than 0 and smaller than a (because its inside the sphere, away from both the center and the surface) i changed the ranges.

dont know if i made it clear or not.

also, i was going to apply that equation, like you said, directly, but when my teacher demonstrated a similar problem in class, he also used those limits, so i guess i got a little mixed up.

thx man