The electric field at a distance of 0.145 m from the surface...

Name: Problem 21, Chapter 22: University Physics with Modern Physics
Uploaded: 2019-08-07T22:29:01-08:00
Duration: 4 min 18 s
Channel: Averell Hause
Description: The electric field at a distance of 0.145 m from the surface of a solid insulating sphere with radius 0.355 m is 1750 N/C. (a) Assuming the sphere's charge is uniformly distributed, what is the charge density inside it? (b) Calculate the electric field inside the sphere at a distance of 0.200 m from the center.

The electric field at a distance of 0.145 m from the surface of a solid insulating sphere with radius 0.355 m is 1750 N/C. (a) Assuming the sphere's charge is uniformly distributed, what is the charge density inside it? (b) Calculate the electric field inside the sphere at a distance of 0.200 m from the center.

Key Concepts

Volume Charge Density

Volume charge density is a measure of how much electric charge exists per unit volume in a material. In problems involving uniformly charged spheres, the total charge can be expressed as the product of the volume charge density and the volume of the sphere. This concept is essential for determining both the enclosed charge within a Gaussian surface and the corresponding electric field.

Electric Field Inside a Charged Sphere

Inside a uniformly charged sphere, the electric field increases linearly with distance from the center because only the charge enclosed by the Gaussian surface contributes to the field at that point. Using Gauss's Law, the electric field is proportional to the radius of the Gaussian surface, which highlights the difference in behavior compared to the external field.

Gauss's Law

Gauss's Law is a fundamental principle in electromagnetism that relates the electric flux through a closed surface to the charge enclosed within that surface. It is particularly useful for calculating electric fields when the system exhibits symmetry, such as spherical symmetry, because it allows the field to be determined without solving complex integrals.

Uniform Charge Distribution

A uniform charge distribution means that the charge density is constant throughout the volume of the object. This simplifies the analysis of the electric field since the charge enclosed within any Gaussian surface is directly proportional to its volume. It also enables the use of symmetrical arguments to apply Gauss’s Law effectively.

Electric Field Outside a Charged Sphere

For a sphere with a uniform charge distribution, the electric field outside the sphere behaves as if the entire charge were concentrated at the center of the sphere. This results from the spherical symmetry and allows the use of the formula for the electric field from a point charge, which greatly simplifies calculations for points located externally.

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