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

Calculate the total charge embodied in a solid with charge density that decreases linearly with height from a value of λ at the bottom to 0 at the top.

Solve for a rectangular prism and a sphere.

2. Relevant equations

∫∫∫ρdxdydz

∫∫∫pr^2sinθdrdθd∅

3. The attempt at a solution

For a rectangular prism, I integrated from 0 to x,y for dx,dy and lambda to 0 for dz. I ended up with Q=x*y*ρ*some function of λ. However, something seems off about this approach, because the charge at any x and y varies with height.

I think if I can get the logic behind the prism, I'll be able to understand the sphere, but any other advice would be helpful.

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# Integral of solids with linearly decreasing charge density

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