# Coulomb's law three points on a line

1. Jun 20, 2014

### Roodles01

1. The problem statement, all variables and given/known data
Three point charges, q1, q2 and q3 all on x-axis (i.e y=0 and z=0)
+q1 at x = 0
-q2 at dist from origin x = a
+q3 at dist from origin x = -2a
where q1, q2 and q3 are magnitudes of the charges.

Assuming q1 = q2 derive magnitude of q3 in order for there to be zero net force on q1.

2. Relevant equations
Coulombs law
F12 = (q1 * q2) / (r12)2 rhat12

3. The attempt at a solution
attempt 1
in order for there to be no force on q1 then,
-q2(a) = q3(2a)
so
q3 = (-q2*a)/2a = -q2/a

bit too simplistic?

or attempt 2
F12 = 1/4*∏*ε0 * (q1*q2) / (r12)2 rhat12 .
F12 = 1/4*∏*ε0 * (q1*q2) / (a2) ex

F13 = 1/4*∏*ε0 * (q1*q3) / (r13)2 * rhat12
F13 = 1/4*∏*ε0 * (q1*q3) / (-2a2) -ex

Resultant
magnitude F1 = 0 = 1/4*∏*ε0 * ((q1*q2) / (a2) ex + (q1*q3) / (-2a2) -ex

agh, run out of input time, will be back
Am I on the right track?

2. Jun 20, 2014

### Staff: Mentor

What does that mean? Charge as function of distance?

That equation cannot be true.

In attempt 2, there are many missing brackets. Apart from that, it looks good.

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