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28. Consider the four particles shown, with q1 = –40.0 µC, q2 = –20.0 µC, q3 = 15.0 µC, and q4 = -25 µC. The square has sides of length a = 25.0 cm. B a 93 a) What is the change in the electric potential energy of the system of the four charges in the configuration shown in the figure if they were originally infinitely far away? b) Charges q3 and q4 are now moved to points A and B, respectively. What is the change in potential energy of the system after these charges are moved? c) What are the magnitude and direction of the electric field at the location of charge q4 due to the other three charges?

28. Consider the four particles shown, with q1 = –40.0 µC, q2 = –20.0 µC, q3 = 15.0 µC, and q4 = -25 µC. The square has sides of length a = 25.0 cm. B a 93 a) What is the change in the electric potential energy of the system of the four charges in the configuration shown in the figure if they were originally infinitely far away? b) Charges q3 and q4 are now moved to points A and B, respectively. What is the change in potential energy of the system after these charges are moved? c) What are the magnitude and direction of the electric field at the location of charge q4 due to the other three charges?

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**Problem 28: Electric Charges and Fields** Consider the four particles shown, with \( q_1 = -40.0 \, \mu \text{C} \), \( q_2 = -20.0 \, \mu \text{C} \), \( q_3 = 15.0 \, \mu \text{C} \), and \( q_4 = -25.0 \, \mu \text{C} \). The square has sides of length \( a = 25.0 \, \text{cm} \). **Diagram Explanation:** The diagram shows four point charges arranged in a square configuration: - \( q_1 \) is at the lower-left corner. - \( q_2 \) is at the upper-left corner. - \( q_3 \) is at the lower-right corner. - \( q_4 \) is initially at the upper-right corner. Points \( A \) and \( B \) are at the positions where \( q_3 \) and \( q_4 \) are moved, respectively, along the x-axis. **Questions:** a) What is the change in the electric potential energy of the system of the four charges in the configuration shown in the figure if they were originally infinitely far away? b) Charges \( q_3 \) and \( q_4 \) are now moved to points \( A \) and \( B \), respectively. What is the change in potential energy of the system after these charges are moved? c) What are the magnitude and direction of the electric field at the location of charge \( q_4 \) due to the other three charges? d) What is the initial acceleration of the charge \( q_4 \) due to the electric force exerted by the other three charges on \( q_4 \) if \( m_4 = 40.0 \, \text{g} \)? e) With what speed is charge \( q_4 \) (with \( m_4 = 40.0 \, \text{g} \)) moving when it is infinitely far away from the other charges? **Note:** This problem involves concepts in electrostatics, including calculations of electric potential energy, electric field, and forces between point charges.
Transcribed Image Text:**Problem 28: Electric Charges and Fields** Consider the four particles shown, with \( q_1 = -40.0 \, \mu \text{C} \), \( q_2 = -20.0 \, \mu \text{C} \), \( q_3 = 15.0 \, \mu \text{C} \), and \( q_4 = -25.0 \, \mu \text{C} \). The square has sides of length \( a = 25.0 \, \text{cm} \). **Diagram Explanation:** The diagram shows four point charges arranged in a square configuration: - \( q_1 \) is at the lower-left corner. - \( q_2 \) is at the upper-left corner. - \( q_3 \) is at the lower-right corner. - \( q_4 \) is initially at the upper-right corner. Points \( A \) and \( B \) are at the positions where \( q_3 \) and \( q_4 \) are moved, respectively, along the x-axis. **Questions:** a) What is the change in the electric potential energy of the system of the four charges in the configuration shown in the figure if they were originally infinitely far away? b) Charges \( q_3 \) and \( q_4 \) are now moved to points \( A \) and \( B \), respectively. What is the change in potential energy of the system after these charges are moved? c) What are the magnitude and direction of the electric field at the location of charge \( q_4 \) due to the other three charges? d) What is the initial acceleration of the charge \( q_4 \) due to the electric force exerted by the other three charges on \( q_4 \) if \( m_4 = 40.0 \, \text{g} \)? e) With what speed is charge \( q_4 \) (with \( m_4 = 40.0 \, \text{g} \)) moving when it is infinitely far away from the other charges? **Note:** This problem involves concepts in electrostatics, including calculations of electric potential energy, electric field, and forces between point charges.
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