What Is the Electric Field at the Surface of a Nucleus with 89 Protons?

[kyin01]

Homework Statement

A certain atom of has 89 protons. Assume that the nucleus is a sphere with radius 7.11e-15 m and with the charge of the protons uniformly spread through the sphere. At the nucleus surface what is the magnitude of the electric field produced by the protons?

Homework Equations

E=F/q

F=(q₁q₂ * 8.99e9)/ d²

a single proton has a charge of 1.6e-19 C

3. The Attempt at a Solution [/b]
So my understanding of the problem is they want me to calculate the electric field at the edge of the nucleus.
so I started my assuming the electric field being at the center of the nucleus with my test charge at the edge of the nucleus. So I did 89 times the charge of a single proton times the constant all divided by the radius squared and I get a number of
2.53e21 N/C

which I am told is wrong, what did I do wrong?

 

[HallsofIvy]

I think this would do better in Physics homework.

 

[Ithryndil]

I believe that's the hard way to do that. You don't really know the force of all the protons. An easier way to do the problem would be to use Gauss's law.

 

[kyin01]

I believe that's the hard way to do that. You don't really know the force of all the protons. An easier way to do the problem would be to use Gauss's law.

I don't think he introduced us that law yet, am i doing it right in the hard way method?

 

[Ithryndil]

I don't think he introduced us that law yet, am i doing it right in the hard way method?

Interesting. When I did it with Gauss's law the answer I got is the same as the answer you got...so why it says it's wrong is beyond me. Perhaps we are both missing something.