Electric Field and total energy

[SamTsui86]

Homework Statement

Two point charges lie along the y axis. A charge of q1 = -12.0 µC is at y = 7.0 m, and a charge of q2 = -2.0 µC is at y = -4.0 m. Locate the point (other than infinity) at which the total electric field is zero.

Homework Equations

E = (K lql) / r^2

The Attempt at a Solution

I setup the two equation make E = 0
so

(K lq1l) / (7-y)^2 = (K lq2l) / (-4+y)^2

It's wrong, please correct my equation

 

[Pyrrhus]

Why do you think that equation is wrong?

 

[SamTsui86]

I think the equation is wrong because I double checked all my math and it said that the answer is wrong.

 

[Pyrrhus]

Ok, Let's review again:

The point in which the electric field will be 0 is between the charges. Because of the standard convention. You picked a point inside so it's correct.

Next we have to set our electric field vectors, such that:

$$\vec{E}_{1} + \vec{E}_{2} = \vec{0}$$

$$\vec{E}_{1} = K \frac{|q_{1}|}{(7-y)^{2}} \vec{j}$$

$$\vec{E}_{2} = -K \frac{|q_{1}|}{(4+y)^{2}} \vec{j}$$

so, the error was using -4, because r will be a distance.