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My goodness have some patience...You can obviously see my typing...
Find the electric field everywhere for a uniformly charged solid sphere that has a radius R and a total charge Q that is uniformly distributed throughout the volume of the sphere that has a charge density \[\rho=\frac QV\], where \[V=\frac 43 \pi R^3\] is the volume of the sphere.
It's an example in my book.
So far I understand that I need to make shell around the charged solid, and use that find the \[\phi_{net}\]
and then we would find the Charge because \[Q=\phi_{net}\epsilon_0\]
From that charge we find the electric field.....
Here is my question
What do they mean by
\[\textrm{For r}\ge R, Q_{inside}=Q\]
\[\textrm{For r}\le R, Q_{inside}=\rho V'\]
They mean that once your shell goes beyond the radius of the charged sphere, the amount of charge inside is constant (obviously, just the total charge of the sphere). But when you're inside, the charge inside your shell is less than that.
"....once your shell goes beyond the radius of the charged sphere, the amount of charge inside is constant..."
" But when you're inside, the charge inside your shell is less than that."
If the shell is INSIDE the sphere, then the charge enclosed is Q times the fraction of the sphere contained in the shell. If the shell is larger than the sphere, though, the total charge inside is just Q.
Actually, insides the sphere the net charge should be zero, because all of the charge lies on the surface; i.e., \( \rho = 0 \).
To see all of this explained, including this case, you might enjoy watching this excellent lecture:
http://ocw.mit.edu/courses/physics/8-02-electricity-and-magnetism-spring-2002/video-lectures/lecture-3-electric-flux-and-gausss-law/
So now...
What do they mean by
For r≥R,Qinside=Q
For r≤R,Qinside=ρV′
What is meant is that when we are outside the sphere, the charge is the entire charge of the sphere Q.
However, once you draw a Gaussian surface inside the sphere, you just want the charge within that surface, which is just the volume of that surface time the charge density.
In other words, the charge outside of the surface is irrelevant.
I think I get it now:
The charge anywhere inside of the charged solid sphere is the density times the newly found volume (which depends on the size of r)
The charge anywhere outside of that charged solid sphere, but still within the shell I have drawn is just Q.