Were is the electric field zero?

[blackblanx]

Homework Statement

What is the net electric field intensity at the origin due to two charges Q1= 2$$\mu$$C at (x=3,y=4) and Q2 = -10$$\mu$$C at (x=6,y=-8). And where should a third charge of magnitude 5 $$\mu$$C be placed so the net electric field at the origin is zero?

Homework Equations

E=KQ/R$$^{2}$$ $$\widehat{r}$$

The Attempt at a Solution

I have found the first part of the question to be E= 3236$$\widehat{i}$$-10069$$\widehat{j}$$ but I am not sure how you would find out were to place the third charge. Please help

 

[tiny-tim]

Hi blackblanx!

(have a mu: µ )

… And where should a third charge of magnitude 5 $$\mu$$C be placed so the net electric field at the origin is zero?
…
I have found the first part of the question to be E= 3236$$\widehat{i}$$-10069$$\widehat{j}$$ but I am not sure how you would find out were to place the third charge. Please help

The third charge will have to supply a field of minus E.

 

[blackblanx]

Hi blackblanx!

(have a mu: µ )


The third charge will have to supply a field of minus E.

but what are the coordinates of where that charge should be placed?

 

[blackblanx]

oh wait never mind i think i got it know thanks it would just be the negative of the electric field vector divided by k(5$$\mu$$C)

 

[blackblanx]

Forget I realized that does not work any ideas of how to find the coordinates?

 

[tiny-tim]

It'll be on the line in the direction of E, at the distance appropriate to the given strength.

 

[blackblanx]

ok thanks