Electromagnetics - Method of Images ?

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Discussion Overview

The discussion revolves around a problem involving the method of images in electromagnetics, specifically concerning a perfectly conducting plane and a uniform infinite line charge. Participants are attempting to find the electric potential and electric field at a specified point in space, while grappling with the implications of the problem's setup and the calculations involved.

Discussion Character

  • Technical explanation
  • Debate/contested
  • Mathematical reasoning

Main Points Raised

  • One participant presents a problem involving a conducting plane and a line charge, seeking assistance in calculating the potential and electric field at a specific point.
  • Another participant questions the absence of a y-component in the electric field calculation, suggesting that the original answer may contain a typo.
  • A participant agrees with the need for a y-component and describes their own calculations, which include contributions from both the line charge and its image, resulting in different values for the electric field and potential than those provided in the original problem.
  • A later reply critiques the clarity of the problem statement, emphasizing the importance of specifying two points for voltage measurement and discussing the conventions for calculating absolute potentials.
  • One participant expresses confusion over the problem's requirements and acknowledges a misunderstanding regarding the reference point for voltage, noting that the conducting plane is defined as having zero potential.

Areas of Agreement / Disagreement

Participants express differing views on the correctness of the provided answers, particularly regarding the electric field components and the calculation of voltage. There is no consensus on the resolution of these discrepancies, and the discussion remains unresolved.

Contextual Notes

Participants highlight potential ambiguities in the problem statement, including the lack of clarity about the reference points for voltage and the implications of the infinite plane in the context of absolute potentials.

s0undmind
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Electromagnetics - Method of Images ?

Hello all, I am in the process of preparing for a entrance examination. In the course of studying I came across this problem that I just can not figure out. Here it is:

A perfectly conducting plane is located in free space at x=4, and a uniform inifinte line charge of 40nC/m lies along the line x=6, y=3 (the intersection of these planes). Let V=0 at the conducting plane. At P(7,-1,5) find (a) V (potential at P); (b) E (electric field at P).

Answer: -316V ; -45.4ax V/m (ax is the unit vector in the x direction)

I have the answers as you can see but I have no idea on how to arrive to them. I have tried for hours. I would appreciate any help or comments.
THank you.
 
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Are you sure about the answer to (b)? It sure seems like there would be a y component to the E-field at (7,-1,5).

What equation do you use to calculate the Electric field due to a charge distribution? Once you have the E field, how do you calculate the voltage V?
 
Thank you for your reply. Well, I started to think about it again and I agree that there should be a y component. I guess it is a typo in the text especially since I was able to calculate a 45.4ax component (corresponding to the egative of x component in the answer) and a 99ay component. I added the electric field contributions from the uniform charge density(at x=6,y=3,z) and its image (at x=2,y=3,z) and obtained this answer.

For the Voltage, I performed an ugly line integral from a point on the conducting surface. I chose a point lying on a normal line from the conducting surface to P(7,-1,5) so that only x would vary in the integral.
After some manipulations and using the wolfram integrator I arrived at the answer of 343.5V, which is close but does not agree with the answer in the text and the sign is wrong. I wonder if there's an easier way to solve this problem. If you have any hints I would like to hear to them.

Thank you.
 
s0undmind said:
Thank you for your reply. Well, I started to think about it again and I agree that there should be a y component. I guess it is a typo in the text especially since I was able to calculate a 45.4ax component (corresponding to the egative of x component in the answer) and a 99ay component. I added the electric field contributions from the uniform charge density(at x=6,y=3,z) and its image (at x=2,y=3,z) and obtained this answer.

For the Voltage, I performed an ugly line integral from a point on the conducting surface. I chose a point lying on a normal line from the conducting surface to P(7,-1,5) so that only x would vary in the integral.
After some manipulations and using the wolfram integrator I arrived at the answer of 343.5V, which is close but does not agree with the answer in the text and the sign is wrong. I wonder if there's an easier way to solve this problem. If you have any hints I would like to hear to them.

Thank you.

I know this thread is old, but I would like to say that this question is poorly explained. A voltage is measured between two points. A voltage is simply a path integral of the E-field between two points (for electrostatic conditions the path taken to get from one point to the other does not matter since the field is conservative...the only thing that matters is the point you start at and the point you end at...YES, this is important). The problem, especially if it is an entrance exam problem, should have specified TWO points that you are finding the voltage between, and at what point you are starting at.

Now, if only one point is specified in the problem and you are to find the voltage there, the other point is taken to be infinity. This is known as an absolute potential. However, you still need to know if you are starting at infinity and moving a test charge to the point, or if you are starting at the point and moving the test charge to infinity. The "convention", which is not clearly explained, is that when finding absolute potentials you start at the point and move the positive test charge to infinity.However, absolute potentials are a little bit ugly when dealing with the theoretical construct of the infinite plane, since the E-field due to an infinite plane of charge is constant everywhere in space, which would yield an absolute potential of -infinity.

EDIT: I am an idiot. It says V=0 at the infinite plane!
 
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