Charge staggered over spherical volume.

[cdummie]

Homework Statement

There is charge placed in a volume of a sphere, whose density changes by expression ρ(r)=ρ₀a/r for 0<r≤a and ρ(0)=0. Where a and ρ₀ are known variables , and r is a distance from the origin. Determine the potential of the point A(0,0,0) with regard to reference point at infinity.

Homework Equations

Gaussian law.

The Attempt at a Solution

I solved it this way:

I separated potential into two parts like this:

since there is different expression for changing of electric field at arbitrary point whose distance from origin is less than a, than for those whose distance is greater than a.

For finding E i used Gaussian law,
and this is what i got for E1:

Doing the same thing for the r greater than a, i got expression for E2 (difference is that i had different limits of integration when finding charge , it was from 0 to a instead of r since i took all of the charge there is):

Placing it into first expression i got:

Now my question is, is this correct, i mean is this correct approach for finding potential in examples like this?

 

[TSny]

Everything looks good!