# Total volumetric charge distribution of the universe

Zee Prime

## Homework Statement

Considering the volumetric density ρv=(e-2r/r2), figure the total charge (ℚ) of the universe.

## Homework Equations

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ρv=ΔQ/ΔV -> (ΔQ ∝ ΔV)
ℚ=∫v ρv dxdydz

## The Attempt at a Solution

I know you can figure it out ℚ when you've a pack of coordinates (bounds of the volume) in which you can calculate the total charge if you find some kind of symetry or not (i.e: cilindric, spherical coordinates and so on); but my mind just stacked overflow when the book asks the total charge of the universe... I wonder what system of coordinates and values should I use for the triple integral?

I've read that the shape of the universe —or known one— is flat; but I'm pretty sure I haven't the proper knowledge and mathematical understanding to realize that; so I assume for early problems, the shape is spherical, so I would use the following:

ℚ=∫vρv dv = ∫∫∫ρvr2Sin(Φ) drdΦdΘ

Jacobian Determinant.

I've found this problem at the second chapter of the book Electromagnetic Theory - Hayt. I'd appreciate some help with this problem. Thank you for your attention and keep this pantheon of physics alive! Congrats on this forum. Related Advanced Physics Homework Help News on Phys.org
phyzguy
I think you've set it up properly. Go ahead and put limits on the integrals and evaluate them.

• Zee Prime
Zee Prime
I think you've set it up properly. Go ahead and put limits on the integrals and evaluate them.
But buddy, how would you put the limits of a spherical-universe (some rate of change?) The book suggest 6.28[C] as a result.

Ty for reply! phyzguy
Ty for reply! 