Gauss' Law with Calculus Video Lessons

Video Thumbnail

Concept

Problem: The electric field at a distance of 0.144 m from the surface of a solid insulating sphere with a radius of 0.384 m is 1710 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 0.223 m from the center.

FREE Expert Solution

In this problem, we're going to consider Gauss's law:

E·dS=qε0, where E is the electric field, S is the surface area enclosing the net charge q, and ε0 is the permeability of free space.

In terms of volume charge density, we can express charge as:

q=ρdV, where V is the volume of the sphere.

A.

Let R be the radius of the sphere and r the radius of the Gaussian surface. 

The volume charge density:

ρ=qV

88% (185 ratings)
View Complete Written Solution
Problem Details

The electric field at a distance of 0.144 m from the surface of a solid insulating sphere with a radius of 0.384 m is 1710 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 0.223 m from the center.

Frequently Asked Questions

What scientific concept do you need to know in order to solve this problem?

Our tutors have indicated that to solve this problem you will need to apply the Gauss' Law with Calculus concept. You can view video lessons to learn Gauss' Law with Calculus. Or if you need more Gauss' Law with Calculus practice, you can also practice Gauss' Law with Calculus practice problems.