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emr564
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Why do I have to integrate? Isn't it redundant?
The volume charge density inside a solid sphere of radius a is given by ρ=ρnaught*r/a, where ρnaught is a constant. Find the total charge as a function of distance r from the center.
Q=ρV
Q=(ρnaught*r/a)*(4/3)(∏a^3)
Q=(4/3)∏ρnaught*r*a^2
but the solution manual says it's supposed to be Q=∏ρnaught*a^3
It says that you have to integrate ρ with respect to V, and that's what confuses me. If you integrate, you're taking the charge of one tiny sphere and adding it the the charge of a concentric sphere a little bigger, so on and so forth, so doesn't that mean that each time you move up to a bigger sphere, you're being redundant? Why can't you multiply the total volume by the charge per volume to get charge?
Homework Statement
The volume charge density inside a solid sphere of radius a is given by ρ=ρnaught*r/a, where ρnaught is a constant. Find the total charge as a function of distance r from the center.
Homework Equations
Q=ρV
The Attempt at a Solution
Q=(ρnaught*r/a)*(4/3)(∏a^3)
Q=(4/3)∏ρnaught*r*a^2
but the solution manual says it's supposed to be Q=∏ρnaught*a^3
It says that you have to integrate ρ with respect to V, and that's what confuses me. If you integrate, you're taking the charge of one tiny sphere and adding it the the charge of a concentric sphere a little bigger, so on and so forth, so doesn't that mean that each time you move up to a bigger sphere, you're being redundant? Why can't you multiply the total volume by the charge per volume to get charge?
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