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

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In summary, the electric field at two points on the X-axis (x=5.0cm and x=10.0cm) is given. It is produced by a single point charge and follows the equation E= kq/r^2. By substituting (x-5) for r^2, a quadratic equation can be obtained. However, solving for the quadratic does not give the correct answer. Using the Coulomb's e field relationship, it is possible to directly relate the two field values and find the charge's location. The further away point will have a smaller electric field magnitude. The distance along the X-axis for the charge's location is 10+X cm.
  • #1
Brit412
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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.
 
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  • #2
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|.
 
  • #3
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!
 
  • #4
Madison029 said:
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.
 

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

1. Where is the charge's location?

The charge's location can be determined by using an appropriate technique, such as electrostatic imaging or magnetic field mapping, to track the movement and distribution of charged particles.

2. How accurate is the method used to find the charge's location?

The accuracy of the method used to find the charge's location depends on various factors, such as the sensitivity of the equipment and the precision of the measurements taken. In general, modern techniques used in scientific research can provide highly accurate results.

3. Can the charge's location change over time?

Yes, the charge's location can change over time as charged particles can move and interact with their environment. It is important to continuously monitor and track the charge's location to accurately understand its behavior.

4. Is it possible to find the charge's location in a vacuum?

Yes, it is possible to find the charge's location in a vacuum using techniques such as ionization or electron bombardment to detect and track the movement of charged particles.

5. How does the charge's location affect its behavior?

The charge's location plays a crucial role in determining its behavior. Charged particles can interact with each other and their environment, and their movement and distribution can affect various physical phenomena, such as electric and magnetic fields. Understanding the charge's location is essential for studying and predicting its behavior.

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