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Introductory Physics Homework Help
Work needed to move alpha particle
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[QUOTE="fruitbubbles, post: 5012000, member: 533690"] [h2]Homework Statement [/h2] 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? [h2]Homework Equations[/h2] W = PE[SUB]o[/SUB]-PE[SUB]f[/SUB] PE (if several point charges) = q[SUB]o[/SUB]*k*Σ(q/r) q[SUB]o[/SUB] will be the alpha particle (2*(1.6*10[SUP]-19[/SUP] C)) , and the other q will be the 4 electrons [h2]The Attempt at a Solution[/h2] [/B] 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[SUP]-[/SUP]/.00707) and then by k and q[SUB]o[/SUB], and get a PE[SUB]o[/SUB] of -2.6*10[SUP]-25[/SUP]J. To get PE[SUB]f[/SUB], 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[SUB]f[/SUB], which I get as -2.66*10[SUP]-25 [/SUP]J (awfully close to the original PE, which seems kinda weird). Then I do W = PE[SUB]o[/SUB]-PE[SUB]f[/SUB] and get 6*10[SUP]-27[/SUP]J of work done, but the answer is -6.08*10^-21 J. I'm not really sure where I went wrong. [/QUOTE]
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Introductory Physics Homework Help
Work needed to move alpha particle
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