Electric Field Due to a Point Charge

[Wables]

Homework Statement

Two particles are fixed to an x axis: particle 1 of charge q1= 2.1 * 10^-8 and particle 2 of charge q2= -4.00q1 at x=70 cm. At what coordinate on the axis is the net electric field produced by the particles equal to zero?

Homework Equations

E_net = E₁ + E₂
E=F/q
F=k q₁q/r²
Let q = point charge in the above formulas

The Attempt at a Solution

E_net = E₁ + E₂ = 0
E₁ = -E₂

k q₁/r₁² = -k q₂/r₂²
q₁/r₁² = q₂/r₂²

At this point I thought I should try to isolate for one of the r values and plug it into a second equation to solve for one of the r values. But there is no other equation I can use to set up a system of equations... or is there? I am stuck here.

All help appreciated,
Thanks!

 

[tiny-tim]

Welcome to PF!

Hi Wables! Welcome to PF!

(try using the X² and X₂ icons just above the Reply box )

At this point I thought I should try to isolate for one of the r values and plug it into a second equation to solve for one of the r values. But there is no other equation I can use to set up a system of equations... or is there?

you need an equation relating r₁ and r₂

 

[supratim1]

use r1 + r2 = x = 70 cm

 

[Wables]

Thanks for the welcome.

r₁+x=20
r₂+x=70

I can use these! Ooooh!

Okay, so:


q₁/r₁²=q₂/r₂²
=> (q₁/q₂)^(1/2)r₂=r₁

Let (q₁/q₂)^(1/2) = z

r₂+x=70
=> r₂=70-x

r₁+x=20
=> zr₂ + x = 20
=> z(70-x) + x = 20
=> x-zx = 20 - 70z

But z is a root of a negative number...?

 

[tiny-tim]

Hi Wables!

q₁/r₁²=q₂/r₂²

No.

Did you draw a diagram?

You need a minus in there, don't you?

 

[Wables]

OH! Haha thanks for catching that. Okay. Thanks for your help, this question was really bugging me! :)