Finding Constants: Potential and Field Analysis

In summary, the speaker is discussing potential and Gauss's law in relation to a problem with a surface charge at x=a. The potential is taken as zero at x=0 and can be found by integrating the field from x=0 to the point. There is no surface charge at x=a. The speaker suggests that the listener may have applied Gauss's law incorrectly and asks for clarification on their working and use of Gaussian surfaces. The speaker also advises to find the field due to charges in (0,a) and (a,2a) and add them together.
  • #1
ermia
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0
Homework Statement
Two infinite conducting plane are a distance 2a away and parrarel. We have constant potentials on the planes. In ##0<x<a## we have charge with density ##\rho## and in ##a<x<2a## with density ##2\rho##. We want to findelectric feild and potential everywhere. And to find the charge density in boundaries.
Relevant Equations
$$\nabla .E=\frac{ \rho}{\epsilon }$$
$$ E=- \nabla V$$
$$Eup -Edown = \sigma / \epsilon$$
I have wrote all feilds and potentials and I want to find the constants.
My first question is " when we say in the a<x<2a the potential is V(x)" then the potential in the a is V(a) or V(0) ( cause it is 0 in our new area) ?
Second one is " when I want to write the gausses law for the point x=a I find two feilds. Does that mean I have another surface charge in x=a?"
 

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  • #2
Potentials are relative to some arbitrary zero. A common convention is to take it as zero at infinity, but that doesn’t work when you an infinite sheet of charge that isn't tending to zero at infinity. Take the potential as zero at x=0.
The potential at any other point can then be found by integrating the field from x=0 to the point. Note that it is necessarily continuous.

There is no surface charge at x=a in the problem.
 
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  • #3
Once I wrote gausses law for the left and write part seperately. I found two different feilds in x=a.
One is ##\frac{ \rho a} {\epsilon }## the other is ## \frac{2 \rho a}{ \epsilon }## thus we can conclude that we have a surface charge in x=a. Where am I wrong?
 
  • #4
ermia said:
Once I wrote gausses law for the left and write part seperately. I found two different feilds in x=a.
One is ##\frac{ \rho a} {\epsilon }## the other is ## \frac{2 \rho a}{ \epsilon }## thus we can conclude that we have a surface charge in x=a. Where am I wrong?
You can be wrong in many places. Most likely, you applied Gauss's law incorrectly. Please post your solution showing a clear picture (a) of the Gaussian surfaces that you used and (b) the equations that you wrote based on Gauss's law. Then we can perhaps figure out where you went wrong. We cannot reverse engineer your mistake from your answers.
 
  • #5
ermia said:
Once I wrote gausses law for the left and write part seperately. I found two different feilds in x=a.
Your attachment is illegible. If you want anyone to check your actual working you will need to type it in, per forum rules. Preferably in LaTeX.
The field at any point is due to all the charges present. Find the field due to the charges in (0,a), the field due to the charges in (a,2a), and add them together.
 
  • #6
haruspex said:
Your attachment is illegible. If you want anyone to check your actual working you will need to type it in, per forum rules. Preferably in LaTeX.
The field at any point is due to all the charges present. Find the field due to the charges in (0,a), the field due to the charges in (a,2a), and add them together.
Thanks. Is my answer right?
$$ \sigma_{left }= 5 \rho a $$
$$ \sigma_{right} = 6 \rho a $$
 

Related to Finding Constants: Potential and Field Analysis

1. What is the purpose of finding constants in potential and field analysis?

The purpose of finding constants in potential and field analysis is to understand and quantify the relationship between electric potential and electric field. This allows scientists to make accurate predictions and calculations about the behavior of electric charges and their interactions.

2. How are constants determined in potential and field analysis?

Constants in potential and field analysis are typically determined through experimentation and mathematical calculations. Scientists can measure electric potential and electric field at different points and use these values to solve for the constant. They may also use known equations and principles, such as Coulomb's Law, to calculate the constant.

3. What are some common units for constants in potential and field analysis?

The units for constants in potential and field analysis depend on the specific constant being measured. Some common units include volts (V) for electric potential, meters (m) for distance, and newtons (N) for force. It is important to pay attention to units when working with constants to ensure accurate calculations.

4. How do constants affect the behavior of electric charges?

Constants play a crucial role in determining the behavior of electric charges. They dictate the strength and direction of the electric field, which influences the movement and interactions of charges. Changes in constants, such as distance or charge magnitude, can greatly impact the behavior of electric charges.

5. Can constants change in different situations?

Yes, constants can change in different situations. For example, the distance between two charges may vary, resulting in a different value for the constant. Additionally, if the charges themselves are different, the constant may also change. It is important to consider the specific situation and adjust constants accordingly for accurate analysis.

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