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1. Three charged particles are arranged in a line, as shown below. Calculate the net electrostatic force on particle `Q_2` due to the other two charges.
1. Three charged particles are arranged in a line, as shown below. Calculate the net electrostatic force on particle Q_2 due to the other two charges.  `F = k(Q_1Q_2)/r^2`
`sum F= 0.5\ N` toward `Q_1`
Given:
`Q_1 = -8.0\ µC = -8.0 times 10^-6\ C`
`Q_2 = +3.0\ µC = +3.0 times 10^-6\ C`
`Q_3 = -4.0\ µC = -4.0 times 10^-6\ C`
Equation:
`F = k(Q_1Q_2)/r^2`
known: `k = 9.0 times 10^9\ N•m^2//C^2`
Solution:
Let `F_(12)` be the positive direction
`sum vec(F) = vec(F)_(12) + vec(F)_(32) = F_(12) - F_(32)`
`F_(12) = k(Q_1Q_2)/(r_(12))^2`
`F_(12) = (k = 9.0 times 10^9\ N•m^2//C^2)((8.0times10^-6\ C)(4.0 times 10^-6\ C))/((0.3\ m))^2`
`F_(12) = 3.2\ N`
`F_(32) = k(Q_2Q_3)/(r_(23))^2`
`F_(32) = (k = 9.0 times 10^9\ N•m^2//C^2)((3.0times10^-6\ C)(4.0 times 10^-6\ C))/((0.2\ m))^2`
`F_(23) = 2.7\ N`
`sum F= F_(13) - F_(23)`
`sum F= (3.2\ N) - (2.7\ N)`
`sum F= 0.5\ N` toward `Q_1` |