A flat conducting sheet of area A has a charge q on each...

A flat conducting sheet of area $A$ has a charge $q$ on each surface. (a) What is the electric field inside the sheet? (b) Use Gauss's law to show that the electric field just outside the sheet is $E=q /\left(\epsilon_{0} A\right)=\sigma / \epsilon_{0} .$ (c) Does this contradict the result of Problem $69 ?$ Compare the field line diagrams for the two situations.

A flat conducting sheet of area $A$ has a charge $q$ on each surface. (a) What is the electric field inside the sheet?
(b) Use Gauss's law to show that the electric field just outside the sheet is $E=q /\left(\epsilon_{0} A\right)=\sigma / \epsilon_{0} .$ (c) Does this contradict the result of Problem $69 ?$ Compare the field line diagrams for the two situations.

Key Concepts

Surface Charge Density

Surface charge density, defined as the charge per unit area on a surface, is key to linking the macroscopic property of total charge with the microscopic distribution of that charge. It directly relates to the discontinuity in the electric field at a boundary between a conductor and its surroundings, leading to an expression where the electric field just outside the surface is proportional to the surface charge density divided by the permittivity of free space.

Electric Field Inside a Conductor

In electrostatics, the electric field within a conductor is zero because the free charges redistribute themselves on the surface to cancel any internal fields. This equilibrium prevents any net electric field from existing inside the conductor, ensuring that the interior remains field-free regardless of external influences.

Gauss's Law

Gauss's law, which states that the net electric flux through any closed surface is equal to the enclosed charge divided by the permittivity of free space, is a powerful tool for calculating electric fields in situations with high symmetry. By choosing an appropriate Gaussian surface that aligns with the symmetry of the charge distribution, it is possible to derive expressions for the electric field in various regions, such as immediately outside a charged surface.

Electric Field Discontinuity at Boundaries

The concept of discontinuity helps in understanding how the electric field changes across a boundary due to surface charges. Specifically, the difference in the electric field just outside versus just inside a conductor is determined by the local surface charge density. This discontinuity is a direct consequence of Gauss's law and is essential for analyzing electric field configurations near charged surfaces.

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