Electrostatics, net force zero?!?

Question

a charge of 6 nanocoulombs and another charge of 3nC are 60cm apart. Where can a 12nC charge be placed where net electrostatic force will cancel out (equal zero)

Answer 1

Coulomb's Law!

Basically, you're finding the distances from the two charges at which another charge can be places to generate a net electrostatic force of 0. Assuming they're all positive, it should be obvious that the only place to put this charge is in between the two.

I apologize first for my bad subscripts and format.

kqq/r1^2 = kqq/r2^2

k(6 nC)(12 nC)/r1^2 = k(3 nC)(12 nC)/r2^2

0.64728/r1^2 = 0.32364/r2^2

2/r1^2 = 1/r2^2

r1^2 = 2r2^2

So the distance from the 6 nC charge is double that of the distance from the 3 nC charge.

So divide the distance between the 2 charges by 3 - 60 cm / 3 = 20 cm.

So:

r1 = 40 cm
r2 = 20 cm