Electrostatic P.E. vs Gravitational P.E.

[zorro]

Homework Statement

I am confused b/w two questions:

1) The mass M of a planet Earth is uniformly distributed over a spherical volume of radius R. Find and expression for the energy needed to disassemble the planet against the gravitational pull amongst its constituent particles.

2) A metal sphere of Radius R has a charge Q. Find its potential energy.

The Attempt at a Solution

In both the cases, we have to find the work done in building the whole setup of radius R.

1) The spherical volume may be supposed to be formed by a large number of their concentric spherical shells. Let's consider that there is a core of radius x at any time. The energy needed to disassemble a spherical shell of thickness dx is

dW= Gm1m2/x

On solving and integrating, we get
W = 3GM²/5R

If I proceed analogously for 2), I get W = 3KQ²/5R which is not correct (unlike 1st)
Where is the error?

 

[LeonhardEuler]

In the planet the mass is uniformly distributed throughout the volume. For a metallic conductor, all the charge is concentrated on the surface.

 

[zorro]

That was quick!
Yeah you are right...I missed that.
Its much more easier to calculate in the case of E.P.E.

Thanks!