To practice Problem-Solving Strategy 21.1 Coulomb\'s Law. Three charged particle

Question

To practice Problem-Solving Strategy 21.1 Coulomb's Law.

Three charged particles are placed at each of three corners of an equilateral triangle whose sides are of length 3.9 cm . Two of the particles have a negative charge: q1 = -6.7 nC and q2 = -13.4 nC . The remaining particle has a positive charge, q3 = 8.0 nC . What is the net electric force acting on particle 3 due to particle 1 and particle 2?

Part B

Find the net force F 3 acting on particle 3 due to the presence of the other two particles. Report you answer as a magnitude F3 and a direction measured from the positive x axis.

Explanation / Answer

F = k*Q3*Q1/3.9^2 = 8.99 * 10^9 * 8 * 10^-9 * 6.7 *10^-9 / (3.9 * 10^-2)^2 = 3.16 * 10^-4 N
F = k*Q3*Q2/3.9^2 =  8.99 * 10^9 * 8 * 10^-9 *13.4 *10^-9 / (3.9 * 10^-2)^2 = 6.34 * 10^-4N

Fx = Fcos(60) + F = (3.16 cos 60 + 6.34 ) * 10 ^4 = 7.92 * 10^-4
Fy = Fsin(60) = 2.74 * 10^-4

To determine magnitude of the net force on a particle,

F = sqrt((7.92 * 10^-4)^2 + (2.74 * 10^-4)^2) = 8.38 * 10^-4 N,

while direction is =arctan(Fy/Fx) = arctan(2.74 / 7.92) = 19.08 degree

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