Finding the point where the net electric field is zero

[rakeru]

Homework Statement

The question wasn't really written down. It was a question asked after an explanation, and it really wasn't straightforward. I'm going to try to make it into a intelligible thing.

If there is a +3 charge and a -1 charge at a distance from one another, where to the right of these two charges would there be a point where the total electric field is zero?
+3 ---------- -1 ----------- P

Homework Equations

E=Qk/r^2

The Attempt at a Solution

I'm not sure if I did the right things but this is what I did:

I named the distance from +3 to P r1 and the distance from -1 to P r2.
If the total electric field must be zero, then I think that the electric field due to +3 must be equal but opposite to the one due to -1. Maybe?
So I put it like this:

E₁=-E₂
Q₁K/r₁^2 = -Q₂K/r₂^2
I canceled out the K.
And for Q₁ I put the +3 charge. For Q₂ I put the -1 charge.

(r₂^2)*3=r₁^2
r₂=√(r₁^2/3)
The question didn't ask from where would the distance be measured, so I picked from the -1 charge.
Would this be right?? Is Q only the magnitude?? Thank you!

 

[hjelmgart]

Yes it is the correct way. And you are always allowed to chose your coordinate system as you wish, it wouldn't change the result.

You could even go further, and simplify it, by saying the charges are a distance, d from each other, and that the distance from the -1 charge to P is r, then you have

3/(r+d)^2 = 1/r^2

Then you can solve it, and find, where the point P is relative to the distance between the two charges.

 

[rakeru]

Yes it is the correct way. And you are always allowed to chose your coordinate system as you wish, it wouldn't change the result.

You could even go further, and simplify it, by saying the charges are a distance, d from each other, and that the distance from the -1 charge to P is r, then you have

3/(r+d)^2 = 1/r^2

Then you can solve it, and find, where the point P is relative to the distance between the two charges.

Oh, okay! Thank you very much! :)