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Q & A: Is the electric field in a conductor really zero?

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Most recent answer: 08/19/2012
We know that for metals relative permittivity is infinite therefore there should be no force of attraction or repulsion between two charges kept in medium of metal, but in case of conductor placed in electric field - 'the free electrons in the conductor drift toward opposite direction of applied electric field resulting in accumulation of electrons on one side and, due to defiency of electrons on other side, positive charge is created.' This is called polarization of metal, this results in creation of an electric field inside the conductor whose direction is opposite to that of applied electric field but both are of equal magnitude, hence they cancel each other and net electric field in the conductor is zero. So my question is that why an electric field is created inside the conductor as there would be no force between charge kept in medium of metal ie. Epsilon-r = Epsilon-m/Epsilon-0, here Epsilon-r is relative permittivity, Epsilon-m is permittivity of medium and Epsilon-0 is absolute permittivity of free space. Coulomb's Law Electrostatic Force is F= Qq/4*pie* Epsilon-0 * r^2.
- Kartik (age 17)
Nagda, Madhya Pradesh, India
It may be a little misleading to think of a conductor as a medium with infinite epsilon. Let's step back a bit and think about the ingredients. There are some electrons in the metal that are free to move. If an electric field is applied very rapidly, the electrons don't at first have time to respond, so until they redistribute the field is present in the metal. (You could think of this effect in terms of a frequency-dependent epsilon, falling off at very high frequency.) Now the electrons flow in response to the field, until, as you say, their distribution makes a field that cancels the applied field inside the metal.

Even at this point, our picture is a bit crude. If there were really no field in the metal, what would keep the electrons piled up on one edge? In actuality some of the field is left over a very short distance scale, called the screening length. On the distance scale the current that would be made by the remaining field is cancelled by the current that would be caused  by other effects of the spatial variation in the electron pile-up.

Mike W.

(published on 08/19/2012)

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