I was doing my homework when I came across this question:
Three equal point charges, each with charge $1.40 \, \rm\mu C$ , are placed at the vertices of an equilateral triangle whose sides are of length $0.250 \,\rm m$. What is the electric potential energy $U$ of the system? (Take the potential energy of the three charges as zero when they are infinitely far apart)
I had been thinking about voltage and electric potential in terms of gravitational potential energy, so I decided to consider the system as a single point charge. I used $$k\frac{q\cdot q}r$$ to get the potential from each charge at the center of the system. This was incorrect. The correct method was to get the potential between each of the charges and add them up.
Why was my approach incorrect? Does calculating gravitational potential energy of a system work the same way? improved formattingWhy?