A particle of charge +2q is placed at the origin and particle of charge -q is placed on the x-axis at x = 2a.Where on the x-axis can a third positive charge be placed so that the net electric force exerted on it is zero?

Question

Quizplus · Accepted Answer

Let the third positive charge be q3 and let it be placed at a distance x from the origin.

The electric force exerted on q3 due to the charge +2q is:

F1 = k(2q)(q3) / x^2

The electric force exerted on q3 due to the charge -q is:

F2 = k(-q)(q3) / (2a - x)^2

The net electric force on q3 is zero when F1 = F2. Substituting the expressions for F1 and F2, we get:

k(2q)(q3) / x^2 = k(-q)(q3) / (2a - x)^2

Simplifying and solving for x, we get:

x = (4/3) a

Therefore, the third positive charge should be placed at a distance of (4/3) a from the origin, which is equivalent to 6.8a. Therefore, the correct answer is B.

A Particle of Charge +2q Is Placed at the Origin