A positive charge Q1 = +4.08 nC is located at x1 = -2.00 m, a negative charge Q2 = -6.50 nC is located at x2 = 3.00 m, and a positive charge Q3 = 4.30 nC is located at x3 = 9.00 m. Find the net potential energy in the field.*1 point-84.25 nJ+84.25 nJ126. 67 nJ105.46 nJ
Question
A positive charge Q1 = +4.08 nC is located at x1 = -2.00 m, a negative charge Q2 = -6.50 nC is located at x2 = 3.00 m, and a positive charge Q3 = 4.30 nC is located at x3 = 9.00 m. Find the net potential energy in the field.*1 point-84.25 nJ+84.25 nJ126. 67 nJ105.46 nJ
Solution
The potential energy U between two charges Q1 and Q2 separated by a distance r is given by the formula:
U = k * Q1 * Q2 / r
where k is Coulomb's constant (8.99 * 10^9 N m^2/C^2).
We have three pairs of charges here: (Q1, Q2), (Q1, Q3), and (Q2, Q3). We need to calculate the potential energy for each pair and then add them up to get the total potential energy.
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For Q1 and Q2: U12 = k * Q1 * Q2 / r12 = (8.99 * 10^9 N m^2/C^2) * (4.08 * 10^-9 C) * (-6.50 * 10^-9 C) / 5.00 m = -5.65 nJ
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For Q1 and Q3: U13 = k * Q1 * Q3 / r13 = (8.99 * 10^9 N m^2/C^2) * (4.08 * 10^-9 C) * (4.30 * 10^-9 C) / 11.00 m = 3.36 nJ
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For Q2 and Q3: U23 = k * Q2 * Q3 / r23 = (8.99 * 10^9 N m^2/C^2) * (-6.50 * 10^-9 C) * (4.30 * 10^-9 C) / 6.00 m = -5.18 nJ
The total potential energy U is the sum of these three values:
U = U12 + U13 + U23 = -5.65 nJ + 3.36 nJ - 5.18 nJ = -7.47 nJ
So, the net potential energy in the field is -7.47 nJ. This option is not listed in your choices. Please check the question or the given options again.
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