A point charge of 5.1 mu C is placed at the origin (x_1 = 0) of a coordinate sys

Question

A point charge of 5.1 mu C is placed at the origin (x_1 = 0) of a coordinate system, and another charge of 1.1 mu C is placed on the x-axis at x_2 = 0.21 m. Where on the x-axis can a third charge be placed in meters so that the net force on it is zero? There are three distinct regions for this problem on the x-axis what are they? Which region must the third charge go in order to make sure the force can vanish? To start with, consider the negative x-axis; the magnitude of the force from the charge at the origin will always be larger than the charge on the other side. Will the force ever vanish on the negative x-axis? What if both charges are positive that is, what if the second charge is 1.1 mu C?

Explanation / Answer

as given both the charges are of opposite charge so the point at which net force is zero , will not present b/w both.

the particle may be placed on the left side or the right side ,

let , Fnet = 0 at x from q1

balance the force,

k*q*q1 / x^2 = k*q*q2 / (x + 0.21)^2

5.1 / x^2 = 1.1 / (x + 0.21)^2

(x + 0.21 / x)^2 = 1.1 / 5.5

(x + 0.21 / x) = 0.464

x = -0.39 m

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