Charge Relaxation in Metals: Explained

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Discussion Overview

The discussion revolves around the concept of charge relaxation in metals, specifically referencing a differential equation derived from Ampere-Maxwell's law and Gauss's law. Participants explore the implications of charge density behavior over time in metallic bodies, considering both free charges and polarization effects.

Discussion Character

  • Technical explanation
  • Conceptual clarification
  • Debate/contested

Main Points Raised

  • Some participants question whether the charge density discussed refers to polarization charges or free charges, noting that polarization charges do not decay as long as an external electric field is present.
  • Others argue that free charges within a metal decay exponentially as they migrate to the surface, leading to a situation where all excess free charge resides on the surface, resulting in zero electric field inside the conductor.
  • A participant suggests that the author's mention of charge relaxation implies that Gauss's law can be simplified to state that the divergence of the electric field equals zero, as all charge migrates to the surface.
  • Another participant confirms that the charge density referred to is indeed free charge, emphasizing that it decreases exponentially while maintaining its shape until fully distributed on the surface.

Areas of Agreement / Disagreement

Participants generally agree that the charge density in question refers to free charge and that it decays exponentially. However, there is some uncertainty regarding the role of polarization charges and the implications of the charge distribution within the metal.

Contextual Notes

There are unresolved aspects regarding the definitions of charge density and the conditions under which the exponential decay occurs, as well as the assumptions about the presence of external electric fields.

mahinda
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I have been using Born and Wolf's Principles of Optics for a project but I don't quite understand the concept of charge relaxation in metals (eq.6, P736 of 7th ed). The author used Ampere-Maxwell's law and Gauss's law to derive a differential equation involving the time differentiation of charge density and the charge density is found to fall off exponentially with time.

I don't quite understand whether this charge density refers to the charges due to polarization, or they really exponentially decay even if the metallic body carries free charges.
 
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mahinda said:
I have been using Born and Wolf's Principles of Optics for a project but I don't quite understand the concept of charge relaxation in metals (eq.6, P736 of 7th ed). The author used Ampere-Maxwell's law and Gauss's law to derive a differential equation involving the time differentiation of charge density and the charge density is found to fall off exponentially with time.

I don't quite understand whether this charge density refers to the charges due to polarization, or they really exponentially decay even if the metallic body carries free charges.

If I understand your question correctly (I don't have a copy of the reference) polarization charges are induced by an external electric field and they don't decay as long as the external field is present. Free charges within a metal decay exponentially in the process of migrating to the metal's surface. Once equilibrium has been attained, all of the excess free charge will reside on the metal object's surface. It arranges itself on the surface so that the electric field at all internal points is zero.
 
Hi, thank you very much! I think I agree with you that the charge density here refers to the free charge. The author's point of mentioning the charge relaxation is that in metals Gauss's law can be considered as divergence of electric field equals zero, since any charge would exponentially decay. I'm not quite sure whether this is because the charges all migrate to the surface so that no charge exists inside the metal.
 
The charge density referred to is free charge. A free charge distribution placed inside a conductor will decrease exponentially in magnitude, while retaining its shape until all the charge is distributed on the surface so that E will be zero inside the conductor.
There will be no charge left inside the conductor at that point.
 

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