Where to Place a Negative Charge for Zero Electric Field at the Origin?

[Bearbull24.5]

Homework Statement

A 40 uC charge is placed on x-axis at x=4cm. Where should a negative 60 uC charge be placed to produce a net electric field of zero at the origin?

Homework Equations

Fe=Ke((q1*q2)/r^2)

The Attempt at a Solution

I tried rearranging this equation to solve for r

 

[zhermes]

Not quite. The idea is that there are two charges, the 40 uC charge is at a particular location, you need to figure out where another one must be placed to make the net field zero at the origin.

How do you find the electric field resulting from two charges?

Conceptually, around where would you guess the other charge should be placed?

 

[Bearbull24.5]

Well I know it has to be located further to the right.

To find the Electric field from 2 charges... it wouldn't be as simple as using the equation E=Ke(q/r^2)?

 

[zhermes]

Well I know it has to be located further to the right.

Totally.

To find the Electric field from 2 charges... it wouldn't be as simple as using the equation E=Ke(q/r^2)?

Not quite. That's the field due to a single point charge. Electric fields obey the principle of 'superposition,' however. To find the net field, you simply add the fields from each individual charge.
Formally:
<br /> E_{net} = \sum_{i=1}^{n} E_i<br />
for n charges