Why Is There No Internal Electric Field in a Neutral Conductor?

[Sheepwall]

Hello, members of physics forums. This is my first post and question. As such, it will be quite basic. In an electric field, a conductor with a neutral total charge is placed. All the charges in the conductor will be on the surface, negative charges against the external electric field, positive charges in the direction the external electric field is pointing.

According to me, there should be an internal electric field; if a negative test charge is placed within the conductor, wouldn't said charge move towards the positive charges on the surface of the conductor? Wouldn't that suggest an internal electric field?

I know that I am wrong. I want to know why I am wrong. Is there a way of not bringing mathematics (unless very basic proportionality) into the explanation; I find it not very pedagogical. (Don't judge, I love mathematics.)

Thanks in advance, fellow earthlings.

 

[UltrafastPED]

For any conductor which is immersed in a static electric field, the induced surface charges will be arranged so that the field internal to the conductor is canceled ... this only takes a few femtoseconds ... if the internal field were not yet cancelled, more of the internal free charges would be shifted so as to accomplish this.

 

[Meir Achuz]

The field lasts for about a nanosecond, by which time the charge has reached the surface, and the interior field is zero.