Question on problem solving approach involving work done

[RoboNerd]

Homework Statement

Homework Equations

I know that U = q * V, so my attempted approach will rely on that method

The Attempt at a Solution

I was wondering if people could help me solve the problem and help me figure out why B is the correct answer and what the pitfall in my problem solving process is.

I define the left proton to me my existing proton that I placed into my 2d space. I then do work to bring an electron and proton.

OK fine.

I define K to be
K = 1 / (4 * pi * epsilon0 )

The potential for the added electron = k * elementary charge / a, with a positive elementary charge due to the fact that the potential references the charge of the initial proton that I placed.

Likewise, the potential for the added proton = k * elementary charge / (2a).

I then multiply the potentials for the proton and the added electron by (-elementary charge) and (-elementary charge) by the equation U = q * V to get the potential energy for the each thing that I brought in.

Thus the potential energy of the added electron = - k * elementary charge^2 / a
and the potential energy of the added proton = k * e^2 / (2a).

Summing them gives me the net potential energy as equalling -k * elementary charge^2 / (2a), which does not equal the answer provided by B.

Could anyone please be kind to guide me into understanding why this approach is incorrect and how the problem could be solved instead?

Thanks for the help in advance!

 

[NascentOxygen]

The second proton experiences fields from two charges when it is moved in.

 

[RoboNerd]

Thanks for the help! I was able to solve it!