Work done to bring together 2 protons

[crazuiee]

Homework Statement

The nucleus of a Helium atom contains 2 protons which are 1.0fm apart. How much work has to be done by an external agent to bring the two protons from an infinite separation to a distance of 1.0fm.

Homework Equations

F=k|q1||q2|/r^2
W=F*r

The Attempt at a Solution

Would i just need to use the charge of a proton to find the force? and then plug it into the work equation?

 

[Delphi51]

The force varies with r, so what force value would you use? You can't even get away with an average value because of the squaring. If you know calculus you can do the integral of F*dr. If not, you'll have to look up a formula for the electric potential energy of a charge at distance r from another charge.

 

[crazuiee]

Would I set the potential energy to the work
and solve for electrical potential energy
so U=-W
U=kq1q2/r

 

[Delphi51]

Yes, that's all you need. U = 0 at infinite distance, so all the work done becomes the U at r = 1 fm.

 

[buffordboy23]

Would I set the potential energy to the work
and solve for electrical potential energy
so U=-W
U=kq1q2/r

Yes, this is somewhat correct. Since there are two protons in your system, U > 0. But your previous equation suggests that the external agent must do negative work, which isn't quite correct b/c protons repulse each other and it should be harder (positive work) to bring them close together. Therefore, your equation U = -W is actually the work done by the electric field. The applied work W_app is W_app = -W = U, so W_app > 0 for this problem.