Potential energy of electricity

[Calpalned]

Homework Statement

I don't understand the answer to part b

Homework Equations

n/a

The Attempt at a Solution

The solution guide skipped too many steps. How was this derived? If the 5th charge is in the middle, it will be equidistant (about $\frac {b\sqrt {2}}{2}$) from each of the other four charges. Did they add up all of the potential energies or do something different? SImply put, I need to see the steps that led to this final answer. Thank you.

 

[gneill]

They added all the potential energies resulting from the new charge's proximity to the existing four charges. Your distance value is good. So just sum the four contributions.