# Help, with finding electron radius for a given condition

1. Oct 12, 2009

### tnutty

1. The problem statement, all variables and given/known data

A classical view of the electron pictures it as a purely electric entity, whose Einstein rest mass energy,E = mc^2 is the energy stored in its electric field.

If the electron were a sphere with charge distributed uniformly over its surface, what radius would it have in order to satisfy this condition? Note: Your answer for the electron's "size" isn't consistent with modern quantum mechanics or with experiments that suggest the electron is a true point particle.

Equations :

E = mc^2
F = qE
F = ma
E_sphere = Q/ (2*pi*r*epsilon_0);
U = 1/2CV^2
U = qV

I am not sure what to equate with E = mc^2 ?

2. Oct 12, 2009

### Delphi51

Do you know calculus? If so you could calculate the work needed to move charge dq in from infinity to the sphere that already has charge q against the electric force repelling dq from q. Then you could integrate that to find the total work done in bringing charge q together. I think it will be W = Q^2/(4*pi*epsilon*r). This is what you set equal to m*c^2.

3. Oct 12, 2009

### tnutty

If I do that then :

r = ke^2 / (m * c^2 );

r = 2.8 fm

But its not correct.

4. Oct 12, 2009

### Delphi51

5. Oct 12, 2009

### tnutty

So the answer seems to be right according to wiki, but masteringPhysics, my online h.w
is not accepting it.

The answer should be in form ____ fm, but its not correct? Any ideas.

6. Oct 13, 2009

### tnutty

Anyone got a clue ?