Electric Field Zero: Find Point Along Y-Axis

[itryphysics]

Homework Statement

A charge of -3.02 micro C is located at the origin abd a charge of -2.44 micro C is located along the y-axis at 2.6109 m. At what point along the y-axis is the electric field zero?

Homework Equations

E = q/ r^2

The Attempt at a Solution

first i determined equations to use for "r" (distance)

r1 = y2 (2.6109m-y)^2
r2 =
I set the electric fields equal to zero

E2-E1 = o

k(2.44 micro C)/(6.8168-6.8168y=y^2) - k(3.02 micro C)/y2 =0

Then i just solved these as a quadratic in the end but the answer under the square root comes out as a negative or as a ridiculously large number. Please guide me through. Much appreciated!

 

[rl.bhat]

k(2.44 micro C)/(6.8168-6.8168y=y^2) - k(3.02 micro C)/y2 =0

Wright this in the following form:
k(2.44 micro C)/(2.6109-y)^2 = k(3.02 micro C)/y^2
Take square root on both side and find the value of y. While writing down the answer you have mention from which charge you are measuring the distance y.

 

[itryphysics]

why should i take the square root. I think the way i solved it and then used the quadratic formula in the end was much easier...

 

[rl.bhat]

(6.8168-6.8168y=y^2)
Check this one.

 

[itryphysics]

oops sorry that was a typo . its (6.8168-6.8168y+y^2)

 

[rl.bhat]

[QUOTE=itryphysics;2041778]oops sorry that was a typo . its (6.8168-6.8168y+y^2)[/QUOTE]

It is also wrong.
(2,6109 - y)^2 = ?. Check it.

 

[itryphysics]

argh! i had a brain spasm i guess...messed up on simple multiplication. Thank you so much for pointing that out!
now i got >> 6.8168-5.2218y+y^2

 

[itryphysics]

so now I think I am going to set two equations equal to each other and then solve for y which will be my distance but I don't know which way i should set it up. Please suggest..

k(2.44 e-6 microC)/ (2.6109-d)^2 = k(3.02 e -6 micro C) / d2

Is it this way or do i need to swap around the denominators? please explain how you figure this out as well. Thanks

 

[rl.bhat]

Yes. Now you can proceed. Still taking square root is more easier.

 

[itryphysics]

so my choice of denominators is correct?

 

[rl.bhat]

When you take square root on both side you get
(2.44 micro C)^1/2/(2.6109-y) = (3.02 micro C)^1/2/y
Now swap around the denominators and solve for y

 

[itryphysics]

for my answer I am getting y= 1.37

I only have one last try left on my online homework program. Can you please check this with your answer to let me know if I committed any errors.Thanks!

 

[rl.bhat]

Your answer is correct.

 

[itryphysics]

your help is greatly appreciated!