I Problem with one of the premises in electrostatic pressure theory

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The discussion centers on the misunderstanding of electric fields within conductors, particularly regarding electrostatic pressure theory. It emphasizes that while the electric field is zero inside a conductor, there exists a thin layer at the surface where the electric field is nonzero and varies from the exterior to zero. This layer has a nonzero volume charge density, contradicting the notion that the electric field is uniformly zero throughout the conductor. The video referenced illustrates how to derive the force per unit area on the surface charge by considering this layer's finite thickness, aligning with Purcell's textbook approach. The conversation highlights the importance of recognizing the nuances in electrostatic behavior near conductor surfaces.
physicsissohard
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I was watching a video and he was trying to derive a result in electrostatic pressure. He was deriving the pressure on a differential area element of a hollow conducting sphere. He did it two ways, the second way was straightforward he did it by using only gauss's law and a neat argument but the first derivation I have a problem.
I have the video linked with the time stamp. . Isn't Electric Field anywhere inside the conductor zero. So there will be no electric field inside the thickness of the conductor. But he managed to integrate it somehow? he considered electric field to be changing inside the conductor that has density rho and did it. But proprties of conductors state that elctric field inside conductor is zero, doesn't it?
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physicsissohard said:
Isn't Electric Field anywhere inside the conductor zero. So there will be no electric field inside the thickness of the conductor. But he managed to integrate it somehow? he considered electric field to be changing inside the conductor that has density rho and did it. But proprties of conductors state that elctric field inside conductor is zero, doesn't it?
The charge at the surface of a conductor in electrostatic equilibrium is not actually in a layer of zero thickness. The surface charge is nonzero within a very thin layer at the surface. There is a nonzero volume charge density and a nonzero electric field within this layer. As you pass through this layer from just outside the conductor, the electric field changes continuously from its value just outside the surface to zero. The electric field is zero everywhere inside the conducting material except for points within this layer.

In many situations, we treat the layer as having zero thickness and model the electric field as having a jump discontinuity at the surface. However, the video shows how to derive the force per unit area on the surface charge of the conductor by treating the layer as having finite thickness. This derivation follows that of Purcell's textbook.
 
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