How to Determine the Location of a Charge from Electric Field Measurements?

[Brit412]

Homework Statement

The electric field at the point x=5.0cm and y=0 points in the positive x direction with a magnitude of 10.0N/C. At the point x=10.0cm and y=0, the electric field points in the positive x direction with a magnitude of 16.0 N/C. Assume this electric field is produced by a single point charge.
Find the charge's location

Homework Equations

E= kq/r^2

The Attempt at a Solution

So my teacher substituted (x-5) for r^2 and got a quadratic equation. I solved for the quadratic but I'm not getting the right answer.

 

[LowlyPion]

Using the Coulomb's e field relationship you should be able to directly relate the 2 field values such that

16*X² = 10*(X+5)²

The product of the distance squared times the field = the same thing.

The one that is further away will have a smaller |E|.

 

[Madison029]

I am having the same problem. Yet out of Coulomb's e Field relationship I get the related field values however when I plus in the appropriate X values they are not equal. I agree that one is further away however that does not determine the charges location.

Thanks much!

 

[LowlyPion]

I am having the same problem. Yet out of Coulomb's e Field relationship I get the related field values however when I plus in the appropriate X values they are not equal. I agree that one is further away however that does not determine the charges location.

Thanks much!

Welcome to PF.

Be careful in what X represents. It is the distance along the X axis from 10 cm. So the location of the charge if that's what you are looking for is at 10 + X cm.