Back to Square One Four point charges form a square with sides of length , as shown in the figure. In the questions that follow, use the constant in place of . Part A What is the electric potential at the center of the square? Make the usual assumption that the potential tends to zero far away from a charge. Hint A.1 How to approach the problem Hint not displayed Hint A.2 Find the distance to the center Hint not displayed Back to Square One Part A Express your answer in terms of , , and appropriate constants. ANSWER: = Correct Part B What is the contribution to the electric potential energy of the system, due to interactions involving the charge ? Hint B.1 Hint not displayed Express your answer in terms of , , and appropriate constants. ANSWER: = Correct Back to Square One Part C What is the total electric potential energy of this system of charges? Hint C.1 How to approach the problem Hint not displayed Hint C.2 How many pairs? Hint not displayed Express your answer in terms of , , and appropriate constants. ANSWER: = Correct Imagine now that charge is released, and it drifts away from the rest of the charges, which remain fixed in place. Part D What would be the kinetic energy of charge at a very large distance from the other charges? Hint D.1 What happens to energy? Hint not displayed Back to Square One Part D Express your answer in terms of , , and appropriate constants. ANSWER: = Correct It should not come as a surprise that the answer to Part D is equal to the intial contribution to the potential energy of the system due to the presence of charge . Initially, the kinetic energy of charge is zero. Because the electric potential between two charges is inversely proportional to the distance between them, after charge has drifted far away from the others, (see B) is (very close to) zero. Since total energy is conserved, the change in potential energy must have been converted into kinetic energy. Part E What will be the potential energy of the system of charges when charge is at a very large distance from the other charges? Hint E.1 Hint not displayed Back to Square One Part D Express your answer in terms of , , and appropriate constants. ANSWER: = Correct There are two ways you could have approached this question. You could have found the sum of the three terms corresponding to the three remaining pairs of charges, or you could have subtracted the initial from the total energy of the system before charge was removed. Electric Potential Ranking Task In the figure there are two point charges, and . There are also six positions, labeled A through F, at various distances from the two point charges. You will be asked about the electric potential at the different points (A through F)....
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