(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

A sphere has outer radius 15 and inner radius 5.

Between r= 5 and 15, the sphere is solid and contains a total charge of 20 C.

At r < 5, the sphere is hollow.

Calculate the electric field at r = 8.

2. Relevant equations

Gauss' Law --> EA = (q)/epsilon zero

3. The attempt at a solution

What I'm confused about is the hollow sphere part. But ignoring that, here's how I would do the problem.

The volume of the entire sphere is (4/3)pi(15^3) = 14137.16694 m^3.

The volume of the hollow part is (4/3)pi(5^3)= 523.598 m^3.

Therefore, the volume of just the solid part is 14137 - 523 = 13613.568 m^3.

The charge density per volume is then 20 / 13613 = 0.001469.

To calculate the electric field at r = 8, I need to find the volume of such a sphere.

Same procedure as above, take the volume minus the empty part to find 1621.06.

Multiply this by the charge density... 1621.06 * 0.001469 to find 2.38133 C.

This is the internal charge.

Take a gaussian surface of radius 8. It will have surface area (4pi)(8^2)

E = (internal charge)/ (epsilon zero)(area)

E= 2.38 / (eps. zero)(804.24) = huge number, 3.34 x 10 ^ 8.

What's confusing me is whether it's ok to take the surface area of a sphere with radius 8, because of that hollow part. Do I need to subtract the hollow part's surface area or something?

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# Homework Help: Electric Field inside a Sphere (Gauss' Law)

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