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## Homework Statement

Four electrons are located at the corners of a square 10.0 nm on a side, with an alpha particle at its midpoint.

How much work is needed to move the alpha particle to the midpoint of one of the sides of the square?

## Homework Equations

W = PE

_{o}-PE

_{f}

PE (if several point charges) = q

_{o}*k*Σ(q/r)

q

_{o}will be the alpha particle (2*(1.6*10

^{-19}C))

, and the other q will be the 4 electrons

## The Attempt at a Solution

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I use the Pytagorean Theorem to find the original distance from each electron to the alpha particle, and I get (.00707 m). Since all four electrons are the same charge and same distance, I multiple 4*(e

^{-}/.00707) and then by k and q

_{o}, and get a PE

_{o}of -2.6*10

^{-25}J. To get PE

_{f}, I calculate the distance, but this time since it will be in the midpoint of one of the sides of the square, the alpha particle will be .005 m from two of the electrons, and again using the Pythagorean Theorem I calculate that it is 0.0112 m from the other two. I plug all that into the equation for PE to get PE

_{f}, which I get as -2.66*10

^{-25 }J (awfully close to the original PE, which seems kinda weird). Then I do W = PE

_{o}-PE

_{f}and get 6*10

^{-27}J of work done, but the answer is -6.08*10^-21 J. I'm not really sure where I went wrong.