Finding point charge location from electric field at two positions

[KatherineK]

Homework Statement

The electric field at the point x=5.00 cm and y=0 points in the positive x direction with a magnitude of 10.0 N/C. At the point x=10.0 cm and y=0, the electric field points in the positive x direction with a magnitude of 15.0 N/C. Assuming the field is produced by a single point charge, find (a) it's location and (b) the sign and magnitude of its charge

Homework Equations

E= kq/r^2

The Attempt at a Solution

1.5E1=E2

1.5 kq / x^2 = kq/ (x-5)^2

1.5(x-5)^2 = x^2

used quadratic, got x=27.2 , assumed charge is positive because E field strength increases as you move in the positive x direction.
BUT I think my reasoning might be wrong..

 

[gabbagabbahey]

Hi KatherineK, welcome to PF!

1.5 kq / x^2 = kq/ (x-5)^2

You might be confusing yourself with this notation; what does the "x" in this equation represent?

Are you assuming that the charge is located along the x-axis (y=0)? If so, what is your reasoning to support this assumption?

 

[KatherineK]

I was making x the distance the charge is from the first electric field (10 N /C)
and yes, I am assuming the charge is on the x axis

 

[gabbagabbahey]

I was making x the distance the charge is from the first electric field (10 N /C)

You should probably use a different variable then, so whoever is marking your assignment doesn't think that you are using it to represent the x-coordinate of the point charge.

and yes, I am assuming the charge is on the x axis

Okay, but why?... If you want full credit for your solutions, you should always support any assumptions you make with reasonable arguments.