# Electric field inside/outside (uniformly charged sphere)

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A sphere of radius a carries a total charge q which is uniformly distributed over the volume of the sphere.

I'm trying to find the electric field distribution both inside and outside the sphere using Gauss Law.

We know that on the closed gaussian surface with spherically symmetric charge distribution Gauss Law states:
$$\frac{q}{ε_0}= \oint \vec{E} \cdot d\vec{A}$$
1. Outside of sphere:
Logically, the charge outside of a sphere will be always on the Gaussian surface and it doesn't change, therefore the electric field outside of a sphere:
$$E=\frac{q}{4πε_0r^{2}}$$
2. Inside of sphere:
Because the charge is symmetrically distributed on the surface and if I image a little sphere with radius r<a inside the sphere with radius r, the little sphere will have less charge on its surface.
$$E=\frac{q \ r}{4πε_0a^{3}}$$
Is this explanation sufficient?
The problem I'm having is that in textbook is written and drawn that the electrical field inside a charged spherical shell = 0.
Isn't sphere = shell (just taking smaller shell for point 2)?
What am I missing?

Last edited:

Ibix
2020 Award
Is the sphere conducting? What effect does the answer have on the charge distribution?

Logically I would think that if I have a conducting sphere the charge is located also inside of a sphere (for example the sphere is made of copper and inside there are also charged particles, but for the insulating one (Iike a thin shell made of metal, but inside is filled with insulator) I suppose the charge will be distributed only on the outer surface, therefore the electric field inside will be 0.

But here I have a problem:
For sphere written up, it is assumed that we have an insulating sphere of radius a.
(http://farside.ph.utexas.edu/teaching/302l/lectures/node30.html)
But by my thinking the electric field inside will be 0, but if I look in the previous post, I see that it is not.

What am I missing?

Ibix
2020 Award
If the charges can move, and they are like charges, where will they go to? It may be easiest to imagine just two free excess charges to start with then add more.

If the charges cannot move, they obviously won't go anywhere.

Which of these is the insulator and which the conductor?

charges can move = conductor
charges cannot move = insulator

Ibix