Question

Two point charges q1 and q2 are 1.30 m apart, and their total charge is 22.9 µC. If the force of repulsion between them is 0.651 N, what are magnitudes of the two charges?

If one charge attracts the other with a force of 0.268N, what are the magnitudes of the two charges if their total charge is also 22.9 nC? The charges are at a distance of 1.30m

Answer 1

Part A (Repel)

Distance between the charges; r = 1.3m

Given

By Coulomb's law Force between them is

The roots of this equation are calculated by the general formula for the form :

Hence solving for we have

Let then

Essentialy the roots of the quadratic equation gives the magnitude of both charges which are 14.3uC and 8.6uC respectively. For a repulsive force we have charges of same sign as expected.

Part B (Attract)

NOTE: I belive that there is a typing error in part 2 that total charge should be 22.9 µC instead of 22.9nC else the roots of the quadratic equation come out to be complex, which is not possible. I am solving for a correct answer.

Distance between the charges; r = 1.3m

Given

(This should be the question)

By Coulomb's law Force between them is

Solving for as in Part A we get,

Let then

Essentialy the roots of the quadratic equation gives the magnitude of both charges which are -24.9µC and 2µC respectively.  For an attractive force we have charges of opposite sign as expected.