Electric potential from electric field at 2 points

[pirates02]

Homework Statement

i have a sphere with center at origin that is partially empty inside with a non-uniform charge. i have 2 arbitrary points outside the sphere. find the difference in potential between the 2 points.

Homework Equations

The Attempt at a Solution

1) find total charge of sphere
2) assume it is a point charge at origin
3) the electric potential is equal at r distance from origin, so i took abs of 2 points and subed it in for distance
3) use the voltage equation (Efield*r), charge being from 1) and distance being from 3)
4) subtract the two to find difference

is something wrong with my steps?
im not writing my step by step throughly puncuated explanation again. auto-log out made me lose it. also stressful week.

 

[rude man]

Seems to me the difficulty is in determining the origin if the charge distribution is completely non-uniform. Like finding the c.m. of a non-uniform-density mass.

Interesting and suspicious that they ask for the difference in potential between two observational points rather than just one. As if there is some coomon-mode term that cancels. Anyone?

 

[pirates02]

er the 'ununiform' was 1/(r^2) uC so technically in a sense the electric field is still equal at X distance from the sphere.

 

[rude man]

You need to state the problem as it was given to you, verbatim et litteratim.

Speaking in spherical coordinates, if the non-uniformity is restricted to r then you're right, and the problem reduces to a simple integration to find the effective q situated at the origin.