Answer to Question #133254 in Physics for Avery

Question

Particles q1 = +8.0 uC, q2= +3.5 uC, and q3= -2.5 uC are in a line. Particles q1 and q2 are separated by 0.10m and particles q2 and q3 are separated by 0.15m. What is the net force on particle q1?

Answer 1

Electric field created by particle of charge $q$ at distance $r$ is $E = \frac{k q}{r^2}$, where $k = 9 \cdot 10^9 N m^2 / C^2$ is Coulomb's constant.

Net electric field, created by charges 2 and 3 at position of charge 1 is $E_{2,3} = k\frac{q_2}{L_1^2} + k\frac{q_3}{(L_1+L_2)^2}$ (actually this is difference, because field created by charge 2 is directed to the left, and by charge 3 to the right, because of the negative charge).

The force acting on charge 1 is hence $F = q_1 E_{2,3} = k q_1 (\frac{q_2}{L_1^2} + \frac{q_3}{(L_1+L_2)^2}) \approx 22.32 N$.