Use of Gauss's Law(Electrostatic)

[Cheetox]

Homework Statement

Charge +q is distributed uniformley throughout a sphere of radius a. Show that the electric field a distance r from the centre of the sphere is as follows

for r less than a E = qr/(4*pi*epsilon0*a^3)
for r greater than E it is the standard equation of and E field around a point charge.

Homework Equations

The Attempt at a Solution

Drawing a gaussian surface inside the sphere I have proved the first part of the question, for the second part my reasoning is as such,
as the charge is distributed uniformley througout the sphere, this results in a constant E field through the sphere, but by gauss's law this means that the charge must form on the surface, thus the sphere can be treated as a point charge which results in the same equation for a point charge as required...is this correct? If not how would I go about the problem?

 

[natugnaro]

Electric field is not constant through the sphere, you found that in part a) .
All charge is not on the surface, "distributed uniformley throughout a sphere of radius a" said text.
But you can apply gauss law for outside of the sphere, just use gaussian surface of radius r>a.