College Physics III – Thermodynamics, Electricity, and Magnetism
Definition
An infinite plane is an idealized two-dimensional surface that extends infinitely in all directions. It is often used to simplify the calculation of electric fields and other physical properties.
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The electric field produced by an infinite plane of charge is uniform and perpendicular to the surface.
The magnitude of the electric field created by an infinite plane of charge is $E = \frac{\sigma}{2\epsilon_0}$, where $\sigma$ is the surface charge density and $\epsilon_0$ is the permittivity of free space.
Gauss's Law can be applied to determine the electric field due to an infinite plane of charge using a cylindrical Gaussian surface.
The concept of an infinite plane helps in simplifying complex problems involving symmetry in electrostatics.
An infinite plane with positive charge creates a uniform electric field pointing away from the plane, while a negatively charged plane creates a field pointing towards it.
Review Questions
What is the expression for the magnitude of the electric field created by an infinite plane of charge?
How does Gauss's Law simplify the calculation of the electric field for an infinite plane?
Describe how the direction of the electric field differs between positively and negatively charged infinite planes.
Related terms
Surface Charge Density: The amount of electric charge per unit area on a surface, denoted by $\sigma$.
Gauss's Law: A law stating that the net flux through any closed surface is equal to $1/\epsilon_0$ times the enclosed electric charge.
Permittivity of Free Space: $\epsilon_0$, a constant representing how much resistance is encountered when forming an electric field in a vacuum. Its value is approximately $8.85 \times 10^{-12} \text{ F/m}$.