- #1
hmparticle9
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- 26
- Homework Statement
- A solid non-conducting sphere of uniform charge density and total charge ##-Q## and radius ##a## is surrounded by a concentric conducting spherical shell of inner radius ##b## and outer radius ##c## with ##a < b < c##. The outer shell has charge##2Q##. I am interested in the case ##r \in [b,c]##
- Relevant Equations
- $$\int_S \mathbf{E} \cdot d \mathbf{S} = \frac{q}{\epsilon_0}$$
The case I am interested in is ##r \in [b,c]##. Because the outer shell is conducting and the outer shell encloses a charge ##-Q## would it be correct to say that for the case ##r \in [b,c)## the charge inside the outer shell arranges itself in a way to "cancel" as much of the contained charge as it can.
Because the outer shell has ##2Q## to play with we are okay. ##Q## of the ##2Q## charge arranges itself on the shell boundary ##r = b##, hence ##E(r) = 0, r \in [b,c)##.
Am I correct in saying that the remaining charge ##Q## arranges on the outer shell ##r=c##? When we use Gauss's law we obtain
$$E(c) = \frac{Q}{4 \pi \epsilon_0 c^2}$$
If we had less than ##Q## charge in the outer shell I am trying to figure out what ##E(r)## would look like in the outer shell...
Because the outer shell has ##2Q## to play with we are okay. ##Q## of the ##2Q## charge arranges itself on the shell boundary ##r = b##, hence ##E(r) = 0, r \in [b,c)##.
Am I correct in saying that the remaining charge ##Q## arranges on the outer shell ##r=c##? When we use Gauss's law we obtain
$$E(c) = \frac{Q}{4 \pi \epsilon_0 c^2}$$
If we had less than ##Q## charge in the outer shell I am trying to figure out what ##E(r)## would look like in the outer shell...
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