College Physics III – Thermodynamics, Electricity, and Magnetism
Definition
A uniformly charged sphere is a three-dimensional object with a spherical shape where the electric charge is distributed evenly throughout the volume of the sphere. This concept is particularly important in the context of understanding Gauss's Law, which describes the relationship between the electric flux through a closed surface and the total electric charge enclosed by that surface.
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For a uniformly charged sphere, the electric field outside the sphere is the same as the electric field of a point charge located at the center of the sphere and having the same total charge as the sphere.
The electric field inside a uniformly charged sphere varies linearly with the distance from the center, with the maximum electric field occurring at the surface of the sphere.
The electric flux through any closed surface surrounding a uniformly charged sphere is proportional to the total charge enclosed by that surface, as described by Gauss's Law.
The electric potential of a uniformly charged sphere is the same as the electric potential of a point charge located at the center of the sphere and having the same total charge as the sphere.
The electric potential energy of a uniformly charged sphere is the same as the electric potential energy of a point charge located at the center of the sphere and having the same total charge as the sphere.
Review Questions
Explain how the electric field outside a uniformly charged sphere is related to the electric field of a point charge with the same total charge.
The electric field outside a uniformly charged sphere is the same as the electric field of a point charge located at the center of the sphere and having the same total charge as the sphere. This is because the sphere's charge is distributed evenly throughout its volume, and from the outside, the sphere behaves as if all the charge is concentrated at a single point at the center. This relationship is a key consequence of Gauss's Law and allows for the simplification of calculations involving the electric field of a uniformly charged sphere.
Describe the variation of the electric field inside a uniformly charged sphere.
The electric field inside a uniformly charged sphere varies linearly with the distance from the center of the sphere. The electric field is zero at the center of the sphere and increases in magnitude as you move towards the surface, with the maximum electric field occurring at the surface of the sphere. This linear variation of the electric field inside the sphere is a unique property that is a direct result of the uniform charge distribution within the sphere, and it is an important concept in understanding the application of Gauss's Law to this type of charge distribution.
Analyze how Gauss's Law can be used to determine the electric flux through a closed surface surrounding a uniformly charged sphere.
Gauss's Law states that the electric flux through any closed surface is proportional to the total charge enclosed by that surface. For a uniformly charged sphere, the electric flux through any closed surface surrounding the sphere is directly proportional to the total charge of the sphere. This is because the charge is distributed evenly throughout the volume of the sphere, and the electric field outside the sphere is the same as the electric field of a point charge located at the center. By applying Gauss's Law, the electric flux can be easily calculated, which is a powerful tool in understanding the behavior of a uniformly charged sphere.
Gauss's Law is a fundamental principle in electromagnetism that relates the electric flux through a closed surface to the total electric charge enclosed by that surface.
Electric Field: The electric field is a vector field that describes the electric force experienced by a charged particle at a given location in space.