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Three charges lie on a line: q1 = +2.0 nC on the left, q2 = +5.0 nC in the middle, and q3 = -3.0 nC on the right. Both q1 and q3 sit 2.0 cm from q2. What is the net electric force on the middle charge q2?
A5.6 x 10^-4 N, toward the right
B5.6 x 10^-4 N, toward the left
C1.1 x 10^-4 N, toward the right
D1.1 x 10^-4 N, toward the left
Answer & Solution
Correct answer: A. 5.6 x 10^-4 N, toward the right
1. Charge q1 is positive and pushes q2 away from itself, which points toward the right, with size k q1 q2 / r^2 = (8.99 x 10^9)(2.0 x 10^-9)(5.0 x 10^-9) / (0.020)^2 = 2.25 x 10^-4 N.
2. Charge q3 is negative and pulls q2 toward itself, which also points toward the right, with size k |q3| q2 / r^2 = (8.99 x 10^9)(3.0 x 10^-9)(5.0 x 10^-9) / (0.020)^2 = 3.37 x 10^-4 N.
3. Both contributions point the same way, toward the right, so they add rather than cancel: 2.25 x 10^-4 N + 3.37 x 10^-4 N = 5.6 x 10^-4 N.
4. The trap is assuming a positive charge on one side and a negative charge on the other must pull the middle charge in opposite directions; here both a push from q1 and a pull from q3 act toward the same side.
_Source: OpenStax Physics (CC BY 4.0), Ch 18 "Static Electricity", section 18.2 Coulomb's law_
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