Why is one of the solutions obtained using Coulomb's Law not valid?

[Saladsamurai]

[SOLVED] Question about Coulomb's Law

I just solved this a problem in my text: Particle 1 of charge +1.0 uC and particle 2 of charge -3.0 uC are held at a separation L=10.0 cm on an x-axis. If particle 3 of unknown charge q3 is to be placed such that the net electrostatic force on it from 1 and 2 is zero, what must its x and y coordinates be?

Okay, I solved this using Coulomb's Law which gave me a quadratic. Thus, I got two solutions. My question is: why is one of them not valid?

I got x=.0366 and x=-.14. -.14 m is the correct answer. Why does the .0366 work? And if it does not, why did the quadratic produce it?

It may be obvious, but I am just not seeing it now.

Thanks

 

[Dick]

It's obvious. A charge of either sign placed between two opposite charges will experience a force from both in the same direction. It has to be outside of the region to be in even unstable equilibrium. Quadratics often give an unphysical solution.

 

[Saladsamurai]

I knew it had to do with the signs. . . I just couldn't put my finger on it. Thanks Dick! Now I know to look for that.

 

[Mamun3680]

Hello !
Can anyone help me to solve the below problem on Coulomb's law please..
One Metal rod with -1000C charge is hanging on the earth. One another charged metal ball which mass 1 kg is tie by a rope & it floating 1m away from the rod. How much charge is containing by the ball??