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I am trying to find the velocity of a charged particle $+q$ as it moves away from a charged shell of charge $+Q$ to a distance of $2R$. I know I need to find the change in electric potential energy but I am confused of a stray minus sign.

This is what I have so far:

$$\Delta U =U_f-U_i=KqQ[\frac{1}{2R}-\frac{1}{R}]=-\frac{KqQ}{2R}$$

So the change in potential energy is negative. However in the answer sheet it states that the change in potential energy is positive. I am not sure what I am missing. Any help would be appreciated. Thank you.

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  • $\begingroup$ Should I be using the formula for potential rather than potential energy? $\endgroup$
    – Jacob Daniels
    Commented Mar 9, 2021 at 15:31
  • $\begingroup$ I have removed my comment ---- Yes you are fine to use potential energy other than potential. $\endgroup$
    – verdelite
    Commented Mar 9, 2021 at 15:44

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I have no comment on your answer sheet; however, consider this: two positively charged particles left alone would move away from each other naturally. In terms of potential energy this is possible if the system moves from a position with higher potential to a new position with lower potential energy, gaining kinetic energy in the process. The difference between final and initial energies is therefore negative.

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