Gauss' Law with Calculus Video Lessons

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:

$\overline{){\mathbf{\oint }}{\mathbf{E}}{\mathbf{·}}{\mathbf{d}}{\mathbf{S}}{\mathbf{=}}\frac{\mathbf{q}}{{\mathbf{\epsilon }}_{\mathbf{0}}}}$, 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:

$\overline{){\mathbf{q}}{\mathbf{=}}{\mathbf{\int }}{\mathbf{\rho }}{\mathbf{d}}{\mathbf{V}}}$, 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:

$\overline{){\mathbf{\rho }}{\mathbf{=}}\frac{\mathbf{q}}{\mathbf{V}}}$

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###### 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.