Question

q1=+10 nC and q2=-5 nC are separated by 0.10 m dinstance. If a third charge q3=2 nC is placed along with the first two charges, where should it be so that the net electric force of q1 and q2 on q3 is zero (0)?

Answer 1

Coulomb law is given by a formula:

$F_{12} = k\frac{q_1q_2}{d^2}$

In this problem:

$F_{13} = k\frac{10*2}{(d+0.1)^2}$

$F_{23} = k\frac{-5*2}{d^2}$

$F_{13}+F_{23}=0$

$\frac{2}{(d+0.1)^2}-\frac{1}{d^2}=0$

$d+0.1 = \sqrt{2}d$

$d = \frac{0.1}{\sqrt{2}-1}$