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A system has 2.00 μC charges at (50 cm, 0) and (−50 cm, 0) and a −1.00 μC charge at (0, 70 cm). As the y-coordinate of the −1.00 μC charge increases, the potential energy ___. As the y-coordinate of the −1.00 μC charge decreases, the potential energy ___.
  1. increases, increases
  2. increases, decreases
  3. decreases, increases
  4. decreases, decreases
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OpenStax College Physics for AP® Courses Solution, Chapter 19, Problem 11 (Test Prep for AP® Courses) (1:59)

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This is College Physics Answers with Shaun Dychko. We have two, two micro-coulomb charges located on the x-axis at negative 50 and positive 50 and then another charge <i>q three</i> of negative one micro-coulomb on the y-axis at a position of 70 centimetres away and the question is as the y-coordinate of this <i>q three</i> increases and it gets farther away, how does the potential energy change and as it gets closer, how does its potential energy change. So, the way I like to answer or think questions like this is that I think about how much kinetic energy could possibly be gained by this charge so if the charge is close to the x-axis or its y-coordinate decreases, then its gonna get closer to these positive charges and its gonna be attracted to these positive charges and… its going to gain kinetic energy as it gets closer and closer to the origin and its maximum kinetic energy will occur here and oops… and now if the thing, if this charge <i>q three</i> is far away, it will get attracted to the origin again but it has further to go and so its going to be accelerating over a greater distance and so it will be gaining greater speed than if it starts close and so it will gain more kinetic energy by starting far away and so that’s another way of saying that’s its potential energy is greater when its farther away because it has the potential for getting more kinetic energy at this far position compared to if it starts close. So, as the y-coordinate increases, the potential energy increases and as the y-coordinate decrease, the potential energy decreases. The answer is B.