Finding total charge from volume charge density

  • Thread starter emr564
  • Start date
  • #1
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Why do I have to integrate? Isn't it redundant?

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?
 
Last edited:

Answers and Replies

  • #2
Spinnor
Gold Member
2,159
362
The charge density is zero at the center and gets larger with increasing r, as you wrote,

ρ=ρnaught*r/a
 
  • #3
6
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Thank you! I finally noticed that after way too long...
 

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