Question

Three charges are arranged in a line. From left to right, the charges are:
Q1= -8mC, Q2 = +3mC and Q3 = -4mC. The distance between Q1 and Q2 is 0.3 m, and the distance between Q2 and Q3 is 0.2 m. Calculate the net electrostatic force on Q3.

how can you find what point Q2 will be at equilibrium. show work

Answer 1

the point where Q2 will be at equilibrium?
The forces on each side are equal and opposite.

Now Q1 is neg, Q2 is positive, so the force on Q2 will be to the left. But Q2 is +, and Q3 is negative, so the force on Q2 will be to the right.
so the idea is to set the two forces MAGNITUDEs equal (you know the directions are opposite already).

KQ1Q2/x^2=KQ2Q3/(.5-x)^2

where you are putting all + charges (you need magnitudes). x is the distance from q1, and .5-x is the distance from Q3.
solve for x

Answer 2

i know how to get to that point. but how would you solve for x. i know you can use the quadratic equation. but im not sure how to