Question

Three particles are fixed on an x axis. Particle 1 of charge q1 is at x =-a, and particle 2 of charge q2 is at x = +a. If their net electrostatic force on particle 3 of charge +Q is to be zero, what must be the ratio q1/g2, when particle 3 is at x 0.480a ?

Answer 1

To find the ratio q1/g2 that results in zero net electrostatic force on particle 3, we equate the forces due to q1 and q2 and solve for the ratio resulting in q1/g2 being equal to 0.2304.

Step-by-step explanation:

Finding the Ratio of Charges for Zero Net Force on a Third Particle

To determine the ratio q1/g2 so that the net electrostatic force on particle 3 is zero when particle 3 is at x = 0.480a, we apply Coulomb's Law. According to Coulomb's Law, the electrostatic force between two charges is directly proportional to the product of the charges and inversely proportional to the square of the distance between them. For the net force on particle 3 to be zero, the force due to charge q1 must be equal in magnitude and opposite in direction to the force due to charge q2.

Let's express the forces in terms of the distances and charges:
F1 = k|q1*Q|/(0.480a)^2
F2 = k|q2*Q|/a^2

Forces F1 and F2 are pointing in opposite directions; thus, for the net force to be zero, |F1| = |F2|. We can equate the magnitudes and solve for the ratio q1/g2 which simplifies to:
q1/g2 = (0.480)^2 = 0.2304