Finding total flux on Gaussian surface

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To find the total electric flux through a Gaussian surface inside a uniformly charged sphere, the total charge Q within the radius r must be considered, as r is less than R. The electric flux is calculated using Gauss's Law, which states that the flux is equal to the enclosed charge divided by the permittivity of free space (ε₀). Since the Gaussian surface is within the sphere, not all of Q contributes to the flux. The assumption is made that the sphere is a non-conductor, which affects the charge distribution. Understanding these concepts is crucial for correctly applying Gauss's Law in this scenario.
phymateng
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Homework Statement


Consider the uniformly charged sphere with radius R. Q is the total charge inside the sphere. Find the total flux passing through the Gaussian surface (spherical shell) with radius r. (r<R)

Homework Equations



I I tried solving for the Electric Flux by simply dividing the Q by Empselon Knot thought this was too simple to be right, and as I suspected it, it was wrong.

The Attempt at a Solution



I used the formula for the electric flux but using Q divided by Empselon Knot and got it wrong. Maybe I'm not getting the concepts right.
 
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Welcome to PF!

Hi phymateng! Welcome to PF! :smile:

(it's called "espilon nought" … oh, and have an epsilon: ε :wink:)

r < R, so the surface is inside the sphere, so it's not all of Q. :smile:
 
Thank you. Yes, Q is the total charge inside the sphere and they are asking me to find the total flux passing through a gaussian surface of radius r inside the sphere. Radius of sphere is R. (so r<R)
 
this solid sphere is a non conductor i assume..right?
 
it doesn't say. So I assume it isn't.
 
The book claims the answer is that all the magnitudes are the same because "the gravitational force on the penguin is the same". I'm having trouble understanding this. I thought the buoyant force was equal to the weight of the fluid displaced. Weight depends on mass which depends on density. Therefore, due to the differing densities the buoyant force will be different in each case? Is this incorrect?

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