Point charge in a conducting plane

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Discussion Overview

The discussion revolves around the configuration of a point charge near a large conducting plane and the validity of using the method of mirror charges to analyze the electric field produced by this setup. Participants explore the implications of grounding the plane and the conditions under which the mirror charge method applies.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants assert that the method of placing mirror charges is correct and simplifies the problem of analyzing the electric field configuration.
  • One participant questions the relevance of the voltage of the plane, suggesting that voltage must be specified relative to another point.
  • Another participant states that the plane must be grounded for the mirror charge method to be valid, implying a condition for the application of this method.
  • One participant clarifies that the plane does not need to be grounded but cannot have a net charge and must be infinite in size for the method to hold.
  • Participants discuss the principle that electric field lines are perpendicular to a conducting plane, which supports the reasoning behind the mirror charge method.

Areas of Agreement / Disagreement

There is no consensus on whether the plane must be grounded for the mirror charge method to be applicable, with competing views on the necessity of grounding and the implications of the plane's charge status.

Contextual Notes

Participants express differing views on the conditions under which the mirror charge method is valid, particularly regarding the grounding of the plane and its charge state. The discussion highlights the need for clarity on the definitions and assumptions involved in the analysis.

sami23
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Point charge +Q is placed close to a very large conducting plane. A professor of physics asserted that the field caused by this configuration is the same as would be obtained by removing the plane and placing a point charge -Q of equal magnitude in the mirror-image position behind the initial position of the plane. Is this correct? Why or why not?
 
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It is correct. The method of placing mirror charges is an easy way to solve such problems.
Experience tells you were to put the charges.
The mathematical way to see this, is by solving the Poisson equation using the correct boundary conditions for the Green function.
 
betel said:
It is correct. The method of placing mirror charges is an easy way to solve such problems.
Experience tells you were to put the charges.
The mathematical way to see this, is by solving the Poisson equation using the correct boundary conditions for the Green function.


Does the voltage of the plane matter?
 
thedore said:
Does the voltage of the plane matter?

What do you mean by voltage? A single plane can not have a voltage, you have to specify in relation to what the voltage is considered. But you can have a charge on the plane.
 
thedore said:
Does the voltage of the plane matter?

Yes,the plane must be grounded

And the mathematical principle behind such "cheating" solution is http://en.wikipedia.org/wiki/Uniqueness_theorem" .
 
Last edited by a moderator:
Actually you want to refer to the theory of images. The plane does not have to be grounded but it cannot have a net charge and it must be infinite in size.

The principle is simple. Electric field lines are perpendicular to a conducting plane. If you mirror the charges on two sides of an imaginary plane (reverse the sign of the charges on opposite sides of the plane) the electric field lines will be perpendicular to the imaginary plane. So mirrored charges produce the same field as charges in front of a mirror. That's how "mirroring" gets it's name.
 
Last edited:

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