Potential energy of electricity

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SUMMARY

The discussion focuses on calculating the potential energy of a fifth charge placed equidistantly among four existing charges. The solution involves summing the potential energies contributed by each of the four charges, considering the distance of approximately ##\frac {b\sqrt {2}}{2}## from the fifth charge to each of the others. The participants emphasize the need for a detailed breakdown of the derivation process to clarify the steps leading to the final answer.

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Homework Statement


I don't understand the answer to part b
Screenshot (41).png


Homework Equations


n/a

The Attempt at a Solution


Screenshot (42).png

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.
 
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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.
 

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